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Titlebook: Integrals and Operators; Irving E. Segal,Ray A. Kunze Book 1978Latest edition Springer-Verlag Berlin Heidelberg 1978 C*-algebra.Hilbert sp

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书目名称Integrals and Operators
编辑Irving E. Segal,Ray A. Kunze
视频video
丛书名称Grundlehren der mathematischen Wissenschaften
图书封面Titlebook: Integrals and Operators;  Irving E. Segal,Ray A. Kunze Book 1978Latest edition Springer-Verlag Berlin Heidelberg 1978 C*-algebra.Hilbert sp
描述TO THE SECOND EDITION Since publication of the First Edition several excellent treatments of advanced topics in analysis have appeared. However, the concentration and penetration of these treatises naturally require much in the way of technical preliminaries and new terminology and notation. There consequently remains a need for an introduction to some of these topics which would mesh with the material of the First Edition. Such an introduction could serve to exemplify the material further, while using it to shorten and simplify its presentation. It seemed particularly important as well as practical to treat briefly but cogently some of the central parts of operator algebra and higher operator theory, as these are presently represented in book form only with a degree of specialization rather beyond the immediate needs or interests of many readers. Semigroup and perturbation theory provide connections with the theory of partial differential equations. C*-algebras are important in har­ monic analysis and the mathematical foundations of quantum mechanics. W*-algebras (or von Neumann rings) provide an approach to the theory of multiplicity of the spectrum and some simple but key elemen
出版日期Book 1978Latest edition
关键词C*-algebra; Hilbert space; Integrals; convergence; differential equation; functional analysis; harmonic an
版次2
doihttps://doi.org/10.1007/978-3-642-66693-3
isbn_softcover978-3-642-66695-7
isbn_ebook978-3-642-66693-3Series ISSN 0072-7830 Series E-ISSN 2196-9701
issn_series 0072-7830
copyrightSpringer-Verlag Berlin Heidelberg 1978
The information of publication is updating

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Basic Integrals, with the integration of the simplest functions on such a space. A full-fledged measure space and the integration of a quite general type of function on such a space will then be derived by a natural species of approximation, in Chap. 3.
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Convergence and Differentiation,o obtain a similarly penetrating theory when the vector space is infinite-dimensional without additional structure in the space. A first step in civilizing a linear space for the purposes of analysis is the introduction of a convenient topology, i.e. one with respect to which relevant operations are
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Function Spaces,eral theory. The primary result in the finite-dimensional case is that the natural injection of . into the dual .** of . is an isomorphism of . onto .**. This means that if . is an element of . and . denotes the element of .** given by the equation .**(.) = .(.) for all . in .*, then the map . → .**
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Invariant Integrals,nd interact with the integration features, so that the additional features cannot really be considered separately. The simplest and most common such additional feature is a topology on the set under consideration, on which the measure in question is defined. Some indications have already been given
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Group Representations and Unbounded Operators,heory to unbounded operators, and related developments in group-representation theory. The theorem of Stone, giving the structure of the general one-parameter continuous unitary group on a Hilbert space, connects with both these matters and is intrinsically important. Its analogs for groups which ar
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