Theory of Linear Operations (Google eBook)

Front Cover
Elsevier, Mar 1, 1987 - Computers - 248 pages
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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.

A new fifty-page section (``Some Aspects of the Present Theory of Banach Spaces'') complements this important monograph.

  

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Contents

Introduction A The LebesgueStieltjes Integral
1
B BMeasurable sets and operators in metric spaces
5
Chapter I Groups
13
Chapter II General vector spaces
17
Chapter III Fspaces
23
Chapter IV Normed spaces
33
Chapter V Banach spaces
49
Chpter VI Compact operators
59
Appendix Weak convergence in Banach spaces
127
Remarks
137
Index of terminology
157
Some aspects of the present theory of Banach spaces
161
Introduotion
163
Chapter I
165
Chapter II Local properties of Banach spaces
169
Chapter III The approximation property and bases
179

Chapter VII Biorthogonal sequences
65
Chapter VIII Linear functionals
71
Chapter IX Weakly convergent sequences
81
Chapter X Linear functional equations
89
Chapter XI Isometry equivalence isomorphism
101
Chapter XII Linear dimension
117
Chapter IV
189
Chapter V Classical Banach spaces
195
Chapter VI
209
Bibliography
217
Additional Bibliography
233
Copyright

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