Abstract
We examine selected topics of the research work of professor Manuel López-Pellicer. After an introductory section, the paper is divided in four main sections, which include his publications on Set Topology, Locally Convex Space Theory, \(C_{p}\)-theory and Descriptive Topology. We shall also glance at his work on Popular Mathematics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Amemiya, I., Kōmura, Y.: Über nicht Vollständige Montel-Räume. Math. Ann. 177, 273–277 (1968)
Angosto, C., Cascales, B.: Measures of weak noncompactness in Banach spaces. Topol. Appl. 156, 1412–1421 (2009)
Angosto, C., Kąkol, J., López-Pellicer, M.: A quantitative approach to weak compactness in Fréchet spaces and spaces C(X). J. Math. Anal. Appl. 403, 13–22 (2013)
Angosto, C., Kąkol, J., Kubzdela, A., López-Pellicer, M.: A quantitative version of Krein’s theorem for Fréchet spaces. Arch. Math. (Basel) 101, 65–77 (2013)
Arias de Reyna, J.: \(\ell _{0}^{\infty }(\varSigma )\) no es totalmente tonelado. Rev. R. Acad. Cienc. Exactas, Fís. Nat. (Esp.) 79, 77–78 (1983)
Arkhangel’skiĭ, A.V.: Topological Function Spaces. Mathematics and Its Applications. Kluwer Academic, Dordrecht (1992)
Asanov, M.O.: On cardinal invariants of spaces of continuous functions. Sovr. Topol. i Teor. Mnozhestv. Izhevsk. 2, 8–12 (1979)
Baars, J., de Groot, J., Pelant, J.: Function spaces of completely metrizable spaces. Trans. Am. Math. Soc. 340, 871–883 (1993)
Blasco Olcina, J.L., López-Pellicer, M.: Algunas propiedades del ejemplo de Tychonoff de un espacio regular que no es completamente regular. Collect. Math. 25, 213–221 (1974)
Bru, R., López-Pellicer, M.: Extensions of algebraic Jordan basis. Glas. Mat. Ser. III 20(40), 289–292 (1985)
Burziyk, J.: On \(K\)-sequences. Czechoslovak Math. J. 43, 1–6 (1993)
Cascales, B., Orihuela, J.: On compactness in locally convex spaces. Math. Z. 195, 365–381 (1987)
Cascales, B., Orihuela, J.: On pointwise and weak compactness in spaces of continuous functions. Bull. Soc. Math. Belg. Ser. B 40, 331–352 (1988)
Cascales, B., Raja, M.: Bounded tightness for weak topologies. Arch. Math. (Basel) 82, 324–334 (2004)
Cascales, B., Kąkol, J., Saxon, S.: Weight of precompact subsets and tightness. J. Math. Anal. Appl. 269, 500–518 (2002)
Cascales, B., Kąkol, J., Saxon, S.: Metrizability versus Fréchet-Urysohn property. Proc. Am. Math. Soc. 131, 3623–3631 (2003)
Christensen, J.P.R.: Topology and Borel Structure: Descriptive Topology and Set Theory with Applications to Functional Analysis and Measure Theory. North-Holland Mathematics Studies, vol. 10. North Holland, Amsterdam (1974)
Díaz, J.C., Florencio, M., Paúl, P.J.: A uniform boundedness theorem for \(L_{\infty }(\mu, X)\). Arch. Math. 60, 73–78 (1993)
Drewnowski, L.: Another note on Kalton’s theorem. Stud. Math. 52, 233–237 (1975)
Drewnowski, L., Florencio, M., Paúl, P.J.: The space of Pettis integrable functions is barrelled. Proc. Am. Math. Soc. 114, 687–694 (1992)
Fabian, M., Hájek, P., Montesinos, V., Zizler, V.: A quantitative version of Krein’s theorem. Rev. Mat. Iberoam. 21, 237–248 (2005)
Ferrando, J.C.: A weakly analytic locally convex space which is not \(K\)-analytic. Bull. Austral. Math. Soc. 79, 31–35 (2009)
Ferrando, J.C.: Some characterizations for \(\upsilon \)X to be Lindelöf \(\varSigma \) or \(K\)-analytic in terms of \({C_{p}}\)(X). Topol. Appl. 156, 823–830 (2009)
Ferrando, J.C., Ferrer, J., López-Pellicer, M.: Strong barrelledness properties in Lebesgue-Bochner spaces. Bull. Belg. Math. Soc. 1, 73–78 (1994)
Ferrando, J.C., Kąkol, J.: On precompact sets in spaces \({C_{c}}\)(X). Georgian Math. J. 20, 247–254 (2013)
Ferrando, J.C., Kąkol, J., López-Pellicer, M.: On a problem of Horvath concerning barrelled spaces of vector valued continuous functions vanishing at infinity. Bull. Belg. Math. Soc. Simon Stevin 11, 127–132 (2004)
Ferrando, J.C., Kąkol, J., López-Pellicer, M.: Bounded tightness conditions for locally convex spaces and spaces C(X). J. Math. Anal. Appl. 297, 518–526 (2004)
Ferrando, J.C., Kąkol, J., López-Pellicer, M.: Necessary and sufficient conditions for precompact sets to be metrizable. Bull. Austral. Math. Soc. 74, 7–13 (2006)
Ferrando, J.C., Kąkol, J., López-Pellicer, M.: A characterization of trans-separable spaces. Bull. Belg. Math. Soc. Simon Stevin 14, 493–498 (2007)
Ferrando, J.C., Kąkol, J., López-Pellicer, M.: A revised closed graph theorem for quasi-Suslin spaces. Czechoslovak Math. J. 59, 1115–1122 (2009)
Ferrando, J.C., Kąkol, J., López-Pellicer, M.: Spaces C(X) with ordered bases. Topol. Appl. 208, 30–39 (2016)
Ferrando, J.C., Kąkol, J., López-Pellicer, M.: On spaces \({C^{b}}\)(X) weakly \(K\)-analytic. Math. Nachr. 290, 2612–2618 (2017)
Ferrando, J.C., Kąkol, J., López-Pellicer, M., Muñoz, M.: Some topological cardinal inequalities for spaces \({C_{p}}\)(X). Topol. Appl. 160, 1102–1107 (2013)
Ferrando, J.C., Kąkol, J., López-Pellicer, M., Saxon, S.A.: Tightness and distinguished Fréchet spaces, J. Math. Anal. Appl. 324, 862–881 (2006)
Ferrando, J.C., Kąkol, J., López-Pellicer, M., Saxon, S.A.: Quasi-Suslin weak duals. J. Math. Anal. Appl. 339, 1253–1263 (2008)
Ferrando, J.C., Kąkol, J., López-Pellicer, M., Śliwa, W.: Web-compact spaces, Fréchet-Urysohn groups and a Suslin closed graph theorem. Math. Nachr. 283, 704–711 (2010)
Ferrando, J.C., López-Pellicer, M.: Una propiedad de M. Valdivia, espacios de tipo \((L)\) y condiciones débiles de tonelación. Rev. R. Acad. Cienc. Exactas, Fís. Nat. (Esp.) 83, 25–34 (1989)
Ferrando, J.C., López-Pellicer, M.: Quasi-suprabarrelled spaces. J. Austral. Math. Soc. (Ser. A) 46, 137–145 (1989)
Ferrando, J.C., López-Pellicer, M.: On ordered suprabarrelled spaces. Arch. Math. (Basel) 53, 405–410 (1989)
Ferrando, J.C., López-Pellicer, M.: Barrelled spaces of class \(n\) and of class \(\aleph _{0}\). Disert. Sem. Mat. Fund. UNED 4 (1992)
Ferrando, J.C., López-Pellicer, M.: Strong barrelledness properties in \(\ell _{0}^{\infty }(X,\mathscr {A})\) and bounded finite additive measures. Math. Ann. 287, 727–736 (1990)
Ferrando, J.C., López-Pellicer, M.: Barrelled spaces of class \(\aleph _{0}\) which are not totally barrelled. Math. Jpn. 37, 465–4471 (1992). Correction, Math. Jpn. 38, 1197–1199 (1993)
Ferrando, J.C., López-Pellicer, M., Sánchez Ruiz, L.M.: Metrizable Barrelled Spaces. Pitman Research Notes in Mathematics Series, vol. 332. Longman Scientific & Technical, London (1995)
Ferrando, J.C., Lüdkovsky, S.V.: Some barrelledness properties of \(c_{0}(\varOmega , X)\). J. Math. Anal. Appl. 274, 577–585 (2002)
Ferrando, J.C., Sánchez Ruiz, L.M.: A maximal class of spaces with strong barrelledness conditions. Proc. R. Irish Acad. 92A, 69–75 (1992)
Ferrando, J.C., Sánchez Ruiz, L.M.: A survey on recent advances on the Nikodým boundedness thorem and spaces of simple functions. Rocky Mt. J. Math. 34, 139–172 (2004)
Ferrando, J.C., Sánchez Ruiz, L.M.: On \(C\)-Suslin spaces. Math. Nachr. 288, 898–904 (2015)
Ferrer, J.R., López-Pellicer, M., Sánchez Ruiz, L.M.: Pták homomorphism theorem revisited. Czechoslovak Math. J. 50, 341–346 (2000)
Franklin, S.P.: Spaces in which sequences suffice II. Fundam. Math. 61, 51–56 (1967)
Gabriyelyan, S.S., Kąkol, J., Kubzdela, A., López-Pellicer, M.: On topological properties of Fréchet locally convex spaces with the weak topology. Topol. Appl. 192, 123–127 (2015)
Gabriyelyan, S.S., Kąkol, J., Leiderman, A.: On topological groups with a small base and metrizability. Fundam. Math. 229, 129–158 (2015)
Gillman, L., Jerison, M.: Rings of Continuous Functions. Van Nostrand, Princeton (1960)
Granero, A.S.: An extension of the Krein-Šmulyan theorem. Rev. Mat. Iberoam. 22, 93–110 (2006)
Hager, A.W.: Some nearly fine uniform spaces. Proc. Lond. Math. Soc. 28, 517–546 (1974)
Isbell, J.R.: Uniform Spaces. American Mathematical Society, Providence (1964)
Kąkol, J., López-Pellicer, M.: On countable bounded tightness for spaces \({C_{p}}\)(X). J. Math. Anal. Appl. 280, 155–162 (2003)
Kąkol, J., López-Pellicer, M.: Compacts coverings for Baire locally convex spaces. J. Math. Anal. Appl. 332, 965–974 (2007)
Kąkol, J., López-Pellicer, M.: On Valdivia strong version of Nikodym boundedness property: J. Math. Anal. Appl. 446, 1–17 (2017)
Kąkol, J., López-Pellicer, M., Okunev, O.: Compact covers and function spaces. J. Math. Anal. Appl. 411, 372–380 (2014)
Kąkol, J., Kubiś, W., López-Pellicer, M.: Descriptive Topology in Selected Topics of Functional Analysis. Developments in Mathematics, vol. 24. Springer, Dordrecht (2011)
Kąkol, J., López-Pellicer, M., Martín-Peinador, E., Tarieladze, V.: Lindelöf spaces C(X) over topological groups. Forum Math. 20, 201–212 (2008)
Kąkol, J., López-Pellicer, M., Moll, S.: Banach disks and barrelledness properties of metrizable \(c_{0}(\varOmega ,X)\). Mediterr. J. Math. 1, 81–91 (2004)
Kąkol, J., López-Pellicer, M., Śliwa, W.: Weakly \(K\)-analytic spaces and the three-spaces property for analyticity. J. Math. Anal. Appl. 362, 90–99 (2010)
Kąkol, J., López Pellicer, M., Todd, A.R.: A topological vector space is Fréchet-Urysohn if and only if it has bounded tightness. Bull. Belg. Math. Soc. Simon Stevin 16, 313–317 (2009)
Köthe, G.: Topological Vector Spaces I. Springer, Heidelberg (1969)
Köthe, G.: Topological Vector Spaces II. Springer, Heidelberg (1979)
Kunzinger, M.: Barrelledness, Baire-like and \(\left( LF\right)\)-Spaces. Pitman Research Notes in Mathematics Series, vol. 298. Longman Scientific & Technical, London (1993)
López-Alfonso, S.: On schachermayer and valdivia results in algebras of Jordan measurable sets. Rev. R. Acad. Cienc. Exactas, Fís. Nat. (Esp.) 110, 799–808 (2016)
López-Alfonso, S., Mas. J., Moll, S.: Nikodym boundedness for webs in \(\sigma \)-algebras. Rev. R. Acad. Cienc. Exactas, Fís. Nat. (Esp.) 110, 711–722 (2016)
López Molina, J.A., López-Pellicer, M.: Sobre la existencia de topologías \(T^{j}\) regulares. Collect. Math. 29, 85–88 (1978)
López-Pellicer, M.: Un ejemplo de un espacio topológico completamente regular que el \(k\)-espacio correspondiente no es completamente regular. Rev. R. Acad. Cienc. Exactas, Fís. Nat. (Esp.) 48, 111–118 (1974)
López-Pellicer, M.: Una nota sobre la propiedad de Blumberg. Rev. R. Acad. Cienc. Exactas, Fís. Nat. (Esp.) 78, 147–150 (1984)
López-Pellicer, M.: Webs and bounded finitely additive measures. J. Math. Anal. Appl. 210, 257–267 (1997)
López-Pellicer, M.: Banach. Historia de la Matemática en el siglo XX. Serie Historia de la Ciencia. Real Academia de Ciencias Exactas, Físicas y Naturales de Madrid, pp. 221–270 (1998)
López-Pellicer, M.: Centenario de John von Neumann (1903–1957). Arbor 175, 9–33 (2003)
López-Pellicer, M.: Presentación de la obra de H. Poincaré (1854–1912). Arbor 178, 621–624 (2004)
López-Pellicer, M.: Matemáticas: Siglo XX y su futuro. Anticipaciones académicas II. Instituto de España. Madrid, pp. 79–148 (2005). ISBN: 84-85559-62-2 y 84-85559-61-4
López-Pellicer, M.: Los protagonistas de los grandes avances científicos. Introducción a la Ingeniería. Limusa (Méjico), pp. 213–264 (2007). ISBN 978-968-18-7161-1
López-Pellicer, M.: Euler: Anécdotas de su vida. Tricentenario del nacimiento de Leonhard Euler (1707-1783), Eds. Alberto Galindo and Manuel López-Pellicer. Instituto de España, pp. 261–276. ISBN 978-84-85559-66-4 (2009)
López-Pellicer, M.: Ramanujan: Un matemático ejemplar para todos. Ciencias.digital 10, 114–125 (2012)
López-Pellicer, M.: Two classes of metrizable spaces \(\ell _{c}\)-invariant. In: Descriptive Topology and Functional Analysis. Springer Proceedings in Mathematics and Statistics, vol. 80, pp. 95–116. Springer, Cham (2014)
López-Pellicer, M.: Recuerdo de Julio Rey Pastor. Rev. R. Acad. Cienc. Exactas, Fís. Nat. (Esp.) 108, 55–72 (2015)
López-Pellicer, M., Bru, R.: Jordan basis for an infinite-dimensional space. Portugal. Math. 43, 153–156 (1985/1986)
López-Pellicer, M., Moll, S.: On suprabarrelledness of \(c_{0}(\varOmega ,X)\). Rev. R. Acad. Cienc. Exactas, Fís. Nat. (Esp.) 97, 37–40 (2003)
López-Pellicer, M., Moll, S.: Unitary sequences and classes of barrelledness. Rev. R. Acad. Cienc. Exactas, Fís. Nat. (Esp.) 97, 367–376 (2003)
López-Pellicer, M., Tarazona, E.: Immersion in products of regular topological spaces. Arch. Math. (Basel) 40, 170–174 (1983)
Mazur, S.: Sur la structure des fonctionelles linéaires dans certains espaces \((L)\). Ann. Soc. Polon. Math. 19, 241 (1946)
Mendoza, J.: Barrelledness conditions on \(S(\varSigma , E)\) and \(B(\varSigma , E)\). Math. Ann. 261, 11–22 (1982)
Mendoza, J.: Necessary and sufficient conditions for C(X, E) to be barrelled or infrabarrelled. Simon Stevin 57, 103–123 (1983)
Michael, E.: \(\aleph _{0}\)-spaces. J. Math. Mech. 15, 983–1002 (1966)
Nagata, J.: On lattices of functions on topological spaces and of functions on uniform spaces. Osaka Math. J. 1, 166–181 (1949)
Narayanaswami, P.P., Saxon, S.A.: \(\left( LF\right)\) spaces, quasi-Baire spaces and the strongest locally convex topology. Math. Ann. 274, 627–641 (1986)
Nikodým, O. M. Sur les familles bornées de fonctions parfaitement additives d’ensembles abstrait. Monatsh. Math. u. Phys. 40, 418–426 (1933)
Nygaard, O.: A remark on Rainwater’s theorem. Ann. Math. Inform. 32, 125–127 (2005)
Pérez Carreras, P., Bonet, J.: Barrelled Locally Convex Spaces. Mathematical Studies, vol. 131. North Holland (1987)
Rainwater, J.: Weak convergence of bounded sequences. Proc. Am. Math. Soc. 14, 999 (1963)
Robertson, N.: The metrisability of precompact sets. Bull. Austral. Math. Soc. 43, 131–135 (1991)
Rodriguez Salinas, B.: Sobre la clase del espacio tonelado \(l_{0}^{\infty }\left( \Sigma \right)\). Rev. R. Acad. Cienc. Exactas, Fís. Nat. (Esp.) 74, 827–829 (1980)
Saxon, S.A.: Nuclear and product spaces, Baire-like spaces and the strongest locally convex topology. Math. Ann. 197, 87–106 (1972)
Saxon, S.A.: Review of the Book: Barrelled Locally Convex Spaces, by P.P. Carreras, J. Bonet. Bulletin (New Series), vol.24, pp. 424–435. American Mathematical Society (1991)
Saxon, S.A., Narayanaswami, P.P.: Metrizable \((LF)\)-spaces, \((db)\)-spaces and the separable quotient problem. Bull. Austral. Math. Soc. 23, 65–80 (1981)
Schachermayer, W.: On some classical measure-theoretic theorems for non-\(\sigma \)-complete Boolean algebras. Dissertationes Math. (Rozprawy Mat.) 214, 1–32 (1982)
Todd, A.R., Saxon, S.A.: A property of locally convex Baire spaces. Math. Ann. 206, 23–34 (1973)
Valdivia, M.: Sobre el teorema de la gráfica cerrada. Collect. Math. 22, 51–72 (1971)
Valdivia, M.: On certain barrelled normed spaces. Ann. Inst. Fourier (Grenoble) 29, 39–56 (1979)
Valdivia, M.: On Suprabarrelled Spaces. In: Functional Analysis, Holomorphy and Approximation Theory. Lecture Notes in Mathematics, vol. 843, pp. 572–580. Springer, Berlin (1981)
Valdivia, M.: Topics in Locally Convex Spaces. Mathematical Studies, vol. 67. North Holland (1982)
Valdivia, M.: On Nikodým boundedness property. Rev. R. Acad. Cienc. Exactas, Fís. Nat. (Esp.) 107, 355–372 (2013)
Valdivia, M., Pérez Carreras, P.: On totally barrelled spaces. Math. Z. 178, 263–269 (1981)
Valov, V.: Function spaces. Topol. Appl. 81, 1–22 (1997)
Wheeler, R.F.: Weak and pointwise compactness in the space of bounded continuous functions. Trans. Am. Math. Soc. 266, 515–530 (1981)
Wilansky, A.: Mazur spaces. Int. J. Math. 4, 39–53 (1981)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Ferrando, J.C. (2019). On the Mathematical Work of Professor Manuel López-Pellicer. In: Ferrando, J. (eds) Descriptive Topology and Functional Analysis II. TFA 2018. Springer Proceedings in Mathematics & Statistics, vol 286. Springer, Cham. https://doi.org/10.1007/978-3-030-17376-0_1
Download citation
DOI: https://doi.org/10.1007/978-3-030-17376-0_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-17375-3
Online ISBN: 978-3-030-17376-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)