Abstract
In this chapter, we shall be concerned with certain basic facts pertaining to strong-, weak- and weak* convergences, including the comparison of the strong notion with the weak notion, e.g., strong- and weak measurability, and strong- and weak analyticity. We also discuss the integration of B-space-valued functions, that is, the theory of Bochner’s integrals. The general theory of weak topologies and duality in locally convex linear topological spaces will be given in the Appendix.
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References for Chapter V
Banach, S. Théorie des Opérations Linéaires, Warszawa 1932.
Dunford, N. (with J. Schwartz) Linear Operators, Vol. II, Interscience 1963.
Hille, E. (with R. S. Phillips) Functional Analysis and Semi-groups. Colloq. Publ. Amer. Math. Soc., 1957. It is the second edition of the book below.
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© 1995 Springer-Verlag Berlin Heidelberg
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Yosida, K. (1995). Strong Convergence and Weak Convergence. In: Functional Analysis. Classics in Mathematics, vol 123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61859-8_6
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DOI: https://doi.org/10.1007/978-3-642-61859-8_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58654-8
Online ISBN: 978-3-642-61859-8
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