Linear Operators: General theory |
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Page 15
( b ) For every pair of distinct points x and y , there are disjoint neighborhoods of x and y . ( c ) For every closed set A , and every x ¢ A , there are disjoint neighborhoods of A and x . ( d ) For every pair of disjoint closed sets ...
( b ) For every pair of distinct points x and y , there are disjoint neighborhoods of x and y . ( c ) For every closed set A , and every x ¢ A , there are disjoint neighborhoods of A and x . ( d ) For every pair of disjoint closed sets ...
Page 320
... the supremum is taken over all finite collections of scalars with oil = 1 and all partitions of E into a finite number of disjoint sets in Σ . A number of elementary properties of the semi - variation are listed in the next lemma .
... the supremum is taken over all finite collections of scalars with oil = 1 and all partitions of E into a finite number of disjoint sets in Σ . A number of elementary properties of the semi - variation are listed in the next lemma .
Page 461
and an arbitrary convex set is possible , provided they are disjoint ( compare Theorem 2.8 ) . He also proved that a convex set K which is compact in the X * topology of the normed linear space X , can be separated from an arbitrary ...
and an arbitrary convex set is possible , provided they are disjoint ( compare Theorem 2.8 ) . He also proved that a convex set K which is compact in the X * topology of the normed linear space X , can be separated from an arbitrary ...
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Contents
Preliminary Concepts | 1 |
The VitaliHahnSaks Theorem and Spaces of Measures | 7 |
B Topological Preliminaries | 10 |
Copyright | |
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Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed closure complex condition Consequently contains continuous functions converges Corollary defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows formula function f given Hence Hilbert space implies integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space linear topological space Math means measure space metric space neighborhood norm open set operator problem Proc projection Proof properties proved range reflexive respect Russian satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero
Bibliographic information
| Title | Linear Operators: General theory Part 1 of Linear Operators, Jacob T. Schwartz Volume 1 of Linear Operators: General Theory. Spectral Theory, Self Adjoint Operators in Hilbert Space. Spectral Operators. I. II. III, William George Bade Volume 7 of Pure & Applied Mathematics : a Wiley-interscience series of texts, monographs & tracts 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 Wiley classics library |
| Authors | Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle |
| Editors | William G. Bade, Robert G. Bartle |
| Contributor | Karreman Mathematics Research Collection |
| Edition | reprint |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of California |
| Digitized | 26 Jun 2018 |
| ISBN | 0470226056, 9780470226056 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |