Keywords
- Compact Group
- Uniform Convergence
- Conditional Expectation
- Continuous Linear Operator
- Converse Implication
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Bibliography
J. Batt, On weak compactness in spaces of vector valued measures and Bochner integrable functions in connection with the Randon Nikodym property of Banach spaces, Revue Roumaine Math. Pures et Appl. 19 (1974), 285–304.
J. Batt and N. Dinculeanu, On the weak compactness criteria of Kolmogorov-Tamarkin and M. Riesz type in the space of Bochner integrable functions over a locally compact group, Measure Theory and Applications, Proceedings, Sherbrook-Canada; Springer Lecture Notes 1033 (1983), 43–58.
J. Bourgain, An averaging result for l 1-sequences and applications to conditionally weakly compact sets in L 1X , Israel J. Math. 32 (1979), 289–298.
J.K. Brooks and N. Dinculeanu, Weak Compactness in spaces of Bochner integrable functions and applications, Advances in Math 24 (1977), 172–188.
_____, Conditional expectations and weak and strong compactness in spaces of Bochner integrable functions, J. Multivariate Analysis, 9 (1979), 420–427.
N. Dinculeanu, Uniform σ-additivity and uniform convergence of conditional expectations in the space of Bochner or Pettis integrable functions, General Toplogy and Modern Analysis, Academic Press (1981), 391–397.
_____, On Kolmogorov-Tamarkin and M. Riesz compactness criteria in function spaces over a locally compact group, J. Math. Analysis and Appl. 89 (1982), 67–85.
_____, Uniform σ-additivity in spaces of Bochner or Pettis integrable functions over a locally compact group, Proc. Amer. Math. Soc. 87 (1983), 627–633.
_____, Weak compactness and uniform convergence of operators in spaces of Bochner integrable functions, J. Math. Analysis and Appl. (to appear).
N. Dinculeanu and C. Ionescu Tulcea, Extensions of certain operators to spaces of abstract integrable functions, Rendiconti del Circolo Mat. Palermo, 31 (1982), 433–448.
A. Grothendrick, Sur les applications lineáires faiblement compactes d'espaces du type C(K), Canad. J. Math. 5 (1983), 129–173.
A. and C. Ionescu Tulcea, Topics in the theory of lifting, Springer, (1969).
A. Kolmogorov, Ueber die Kompaktheit der Funktionenmengen bei der Konvergenz in Mittel, Nachr. Acad. Wiss. Gőttingen Math.-Phys. Kl. II (1931), 60–63.
M. Nicolescu, Analiza Matematica, vol III. Ed. Technica, Bucarest, 1960.
M. Riesz, Sur les ensembles compacts de functions sommables, Acta Litt. Sci. Univ. Szeged 6 (1933), 136–142.
J.D. Tamarkin, On the compactness of the space L, Bull. Amer. Math. Soc. 38 (1932), 79–84.
A. Weil, L'Intégration dans les groupes topologigues et ses applications, Hermann, Paris, 1953.
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© 1985 Springer-Verlag
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Dinculeanu, N. (1985). Characterization of weak compactness in function spaces by means of uniform convergence of extended operators. In: Kalton, N.J., Saab, E. (eds) Banach Spaces. Lecture Notes in Mathematics, vol 1166. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074690
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DOI: https://doi.org/10.1007/BFb0074690
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