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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S. Banach [1], N. Dunford-J. Schwartz [1] and E. Hille-R. S. Phillips [1],
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© 1974 Springer-Verlag Berlin Heidelberg
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Yosida, K. (1974). Strong Convergence and Weak Convergence. In: Functional Analysis. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, vol 123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-96208-0_6
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DOI: https://doi.org/10.1007/978-3-642-96208-0_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-96210-3
Online ISBN: 978-3-642-96208-0
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