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Quotient spaces of Banach lattices and Marcinkiewicz spaces

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Literature Cited

  1. E. V. Tokarev “Quotient spaces of Marcinkiewicz spaces,” Sib. Mat. Zh.,19, No. 3, 704–707 (1978).

    Google Scholar 

  2. M. M. Day, Normed Linear Spaces, Springer-Verlag, Berlin (1962).

    Google Scholar 

  3. A. Grothendieck, “Sur les applications lineaires faiblement compactes d'espaces du type C(K),” Can. J. Math.,5, 129–173 (1953).

    Google Scholar 

  4. H. P. Rosenthal, “On complemented and quasicomplemented subspaces of quotients of C(S) for Stonian S,” Proc. Nat. Acad. Sci. USA,60, 1165–1169 (1968).

    Google Scholar 

  5. L. V. Kantorovich and G. P. Akilov, Functional Analysis [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  6. J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces, II, Function Spaces, Springer-Verlag, Berlim (1979).

    Google Scholar 

  7. B. Z. Vulikh, Introduction to the Theory of Partially Ordered Spaces, Wolters Noordhoff, Groningen (1967).

    Google Scholar 

  8. P. S. Uryson, Works on Topology and Other Fields of Mathematics [in Russian], Vol. 2, Gostekhizdat, Moscow (1951).

    Google Scholar 

  9. A. V. Bukhvalov, A. I. Veksler, and G. Ya. Lozanovskii, “Banach lattices-some Banach aspects of the theory,” Usp. Mat. Nauk,34, No. 2, 138–183 (1979).

    Google Scholar 

  10. Cz. Bessaga and A. Pelczynski, “On bases and unconditional convergence of series in Banach spaces,” Stud. Math.,17, 151–164 (1958).

    Google Scholar 

  11. H. P. Rosenthal, “A characterization of Banach spaces containingZ 1,” Proc. Nat. Acad. Sci. USA,71, 2411–2413 (1974).

    Google Scholar 

  12. S. Karlin, “Bases in Banach spaces,” Duke Math. J.,15, 971–985 (1948).

    Google Scholar 

  13. R. Haydon, Sur les espaces de Banach réticulés injectifs, Séminaire Choquet,16, 1976/77, Initiation à l'analyse, p. 14/01–14/02 (1978).

    Google Scholar 

  14. V. Sh. Khasanov, “On the spaces C(H) with the Grothendieck property,” in: Materials of the Fifth Scientific Conference on Mathamatics, Tomsk State Univ. (1975), pp. 32–33.

  15. E. V. Tokarev, “On subspaces of certain symmetric function spaces,” Teor. Funktsii Funktsional. Anal. Prilozhen., No. 24, 156–161 (1975).

    Google Scholar 

  16. S. G. Krein, Yu. I. Petunin, and E. M. Semenov, Interpolation of Linear Operators [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  17. G. Ya. Lozanovskii, “On localized functionals in vector lattices,” Teor. Funktsii Funktsional. Anal. Prilozhen., No. 19, 66–80 (1974).

    Google Scholar 

  18. A. Pelczynski and W. Szlenk, “An example of a nonshrinking basis,” Rev. Roumaine Math. Pures Appl.,10, No. 7, 961–966 (1965).

    Google Scholar 

  19. H. P. Rosenthal, “On injective Banach spaces and the spaces L(μ) for finite measure μ,” Acta Math.,124, No. 3–4, 205–248 (1970).

    Google Scholar 

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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 25, No. 2, pp 205–212, March–April, 1984.

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Tokarev, E.V. Quotient spaces of Banach lattices and Marcinkiewicz spaces. Sib Math J 25, 332–338 (1984). https://doi.org/10.1007/BF00971471

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