Linear Operators: General theory |
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Page 20
A sequence { an } in a metric space is a Cauchy sequence if limm , glam , an ) = 0. If every Cauchy sequence is convergent , a metric space is said to be complete . The next three lemmas are immediate consequences of the definitions .
A sequence { an } in a metric space is a Cauchy sequence if limm , glam , an ) = 0. If every Cauchy sequence is convergent , a metric space is said to be complete . The next three lemmas are immediate consequences of the definitions .
Page 68
which converges weakly to a point in X. Every sequence { xn } such that { x * xn } is a Cauchy sequence of scalars for each x * e X * is called a weak Cauchy sequence . The space X is said to be weakly complete if every weak Cauchy ...
which converges weakly to a point in X. Every sequence { xn } such that { x * xn } is a Cauchy sequence of scalars for each x * e X * is called a weak Cauchy sequence . The space X is said to be weakly complete if every weak Cauchy ...
Page 345
Show that a sequence of functions in A ( D ) is a weak Cauchy sequence ( a sequence converging weakly to f in A ( D ) ) if and only if it is uniformly bounded and converges at each point of the boundary of D ( to f ) .
Show that a sequence of functions in A ( D ) is a weak Cauchy sequence ( a sequence converging weakly to f in A ( D ) ) if and only if it is uniformly bounded and converges at each point of the boundary of D ( to f ) .
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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 |