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Theory of Linear Operations
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General Information
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Type.................: Ebook
Part Size............: 9,958,001 bytes
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Posted by............: ~tqw~
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Release Notes
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This classic work by the late Stefan Banach has been translated into English so
as to reach a yet wider audience. It contains the basics of the algebra of
operators, concentrating on the study of linear operators, which corresponds to
that of the linear forms a1x1 • a2x2 • ... • anxn of algebra.
The book gathers results concerning linear operators defined in general spaces
of a certain kind, principally in Banach spaces, examples of which are: the
space of continuous functions, that of the pth-power-summable functions, Hilbert
space, etc. The general theorems are interpreted in various mathematical areas,
such as group theory, differential equations, integral equations, equations with
infinitely many unknowns, functions of a real variable, summation methods and
orthogonal series.
Table of Contents
The Lebesgue-Stieltjes Integral.
(B)-Measurable Sets and Operators in Metric Spaces.
Groups.
General Vector Spaces.
F-Spaces.
Normed Spaces.
Banach Spaces.
Compact Operators.
Biorthogonal Sequences.
Linear Functionals.
Weakly Convergent Sequences.
Linear Functional Equations.
Isometry, Equivalence, Isomorphism.
Linear Dimension.
Appendix: Weak Convergence in Banach Spaces.Some Aspects of the Present Theory
of Banach Spaces
Reflexive and Weakly Compactly Generated Banach Spaces.
Related Counter Examples.
Local Properties of Banach Spaces.
The Approximation Property and Bases.
Characterizations of Hilbert Spaces in the Class of Banach Spaces.
Classical Banach Spaces.
The Topological Structure of Linear Metric Spaces.
Bibliography.
Product Details
* ISBN: 0444701842
* ISBN-13: 9780444701848
* Format: Hardcover, 248pp
* Publisher: Elsevier Science & Technology Books
* Pub. Date: March 1987
* Edition Number: 2
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