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Page 494
2 we conclude that T * maps the unit sphere of X * into a conditionally weakly
compact set of rca ( S ) , and therefore T * is a weakly compact operator . By
Theorem 4 . 8 this implies that T is a weakly compact operator . Q . E . D . 4
THEOREM .
2 we conclude that T * maps the unit sphere of X * into a conditionally weakly
compact set of rca ( S ) , and therefore T * is a weakly compact operator . By
Theorem 4 . 8 this implies that T is a weakly compact operator . Q . E . D . 4
THEOREM .
Page 541
compact and compact operators from L ( S ) to an arbitrary space X . Phillips [ 3 ]
treated the same case for an arbitrary o - finite measure space X obtaining a
representation of the general operator as an integral with respect to a
Lipschitzean ...
compact and compact operators from L ( S ) to an arbitrary space X . Phillips [ 3 ]
treated the same case for an arbitrary o - finite measure space X obtaining a
representation of the general operator as an integral with respect to a
Lipschitzean ...
Page 577
Spectral Theory of Compact Operators It has been observed in some of the
exercises in Section VI . 9 that a number of linear operators of importance in
analysis either are compact , or have compact squares . The structure of the
spectrum of ...
Spectral Theory of Compact Operators It has been observed in some of the
exercises in Section VI . 9 that a number of linear operators of importance in
analysis either are compact , or have compact squares . The structure of the
spectrum of ...
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Contents
Special Spaces | 237 |
Convex Sets and Weak Topologies | 409 |
General Spectral Theory | 555 |
Copyright | |
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Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad domain elements equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math mean measure space metric space neighborhood norm operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero
Bibliographic information
| Title | Linear Operators: General theory Part 1 of Linear Operators, Jacob T. Schwartz Volume 1; Volume 7 of Pure and applied mathematics : a series of texts and monographs Volume 7 of Pure and applied mathematics Interscience Press Pure and applied mathematics, ISSN 0079-8185 |
| Authors | Nelson Dunford, Jacob T. Schwartz |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of Michigan |
| Digitized | 20 Nov 2007 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |