Overview
- Authors:
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Paul Richard Halmos
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Indiana University, Bloomington, USA
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Viakalathur Shankar Sunder
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University of California, Santa Barbara, USA
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Table of contents (17 chapters)
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- Paul Richard Halmos, Viakalathur Shankar Sunder
Pages 1-3
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- Paul Richard Halmos, Viakalathur Shankar Sunder
Pages 4-7
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- Paul Richard Halmos, Viakalathur Shankar Sunder
Pages 8-16
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- Paul Richard Halmos, Viakalathur Shankar Sunder
Pages 17-20
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- Paul Richard Halmos, Viakalathur Shankar Sunder
Pages 21-26
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- Paul Richard Halmos, Viakalathur Shankar Sunder
Pages 27-31
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- Paul Richard Halmos, Viakalathur Shankar Sunder
Pages 32-38
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- Paul Richard Halmos, Viakalathur Shankar Sunder
Pages 39-42
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- Paul Richard Halmos, Viakalathur Shankar Sunder
Pages 43-49
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- Paul Richard Halmos, Viakalathur Shankar Sunder
Pages 50-58
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- Paul Richard Halmos, Viakalathur Shankar Sunder
Pages 59-71
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- Paul Richard Halmos, Viakalathur Shankar Sunder
Pages 72-75
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- Paul Richard Halmos, Viakalathur Shankar Sunder
Pages 76-84
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- Paul Richard Halmos, Viakalathur Shankar Sunder
Pages 85-94
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- Paul Richard Halmos, Viakalathur Shankar Sunder
Pages 95-104
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- Paul Richard Halmos, Viakalathur Shankar Sunder
Pages 105-110
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- Paul Richard Halmos, Viakalathur Shankar Sunder
Pages 111-118
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Back Matter
Pages 119-134
About this book
The subject. The phrase "integral operator" (like some other mathematically informal phrases, such as "effective procedure" and "geometric construction") is sometimes defined and sometimes not. When it is defined, the definition is likely to vary from author to author. While the definition almost always involves an integral, most of its other features can vary quite considerably. Superimposed limiting operations may enter (such as L2 limits in the theory of Fourier transforms and principal values in the theory of singular integrals), IJ' spaces and abstract Banach spaces may intervene, a scalar may be added (as in the theory of the so-called integral operators of the second kind), or, more generally, a multiplication operator may be added (as in the theory of the so-called integral operators of the third kind). The definition used in this book is the most special of all. According to it an integral operator is the natural "continuous" generali zation of the operators induced by matrices, and the only integrals that appear are the familiar Lebesgue-Stieltjes integrals on classical non-pathological mea sure spaces. The category. Some of the flavor of the theory can be perceived in finite dimensional linear algebra. Matrices are sometimes considered to be an un natural and notationally inelegant way of looking at linear transformations. From the point of view of this book that judgement misses something.
