Linear Operators, Part 1 |
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Page 68
The space X is said to be weakly complete if every weak Cauchy sequence has a
weak limit . In Chapter V , a topology is introduced in certain linear spaces in
such a way that they become Hausdorff spaces in which the notion of
convergence ...
The space X is said to be weakly complete if every weak Cauchy sequence has a
weak limit . In Chapter V , a topology is introduced in certain linear spaces in
such a way that they become Hausdorff spaces in which the notion of
convergence ...
Page 293
It follows from Lemma II.3.27 that K is bounded . If the integrals Set ( s ) u ( ds )
are not countably additive uniformly with respect to f in K there is a number ε > 0 ,
a decreasing sequence En e { with a void limit , and functions in in K such that le
...
It follows from Lemma II.3.27 that K is bounded . If the integrals Set ( s ) u ( ds )
are not countably additive uniformly with respect to f in K there is a number ε > 0 ,
a decreasing sequence En e { with a void limit , and functions in in K such that le
...
Page 658
Nelson Dunford, Jacob T. Schwartz. travel thousands of feet and recoil from the
wall millions of times . Thus , from the physical point of view , the time T involved
in the experiment is large enough to give a good value for the limit 1 ( iii ) lim T 00
...
Nelson Dunford, Jacob T. Schwartz. travel thousands of feet and recoil from the
wall millions of times . Thus , from the physical point of view , the time T involved
in the experiment is large enough to give a good value for the limit 1 ( iii ) lim T 00
...
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Contents
Preliminary Concepts | 1 |
The VitaliHahnSaks Theorem and Spaces of Measures | 7 |
B Topological Preliminaries | 10 |
Copyright | |
87 other sections not shown
Common terms and phrases
Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed complex Consequently contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero
Bibliographic information
| Title | Linear Operators, Part 1 Linear Operators, Jacob T. Schwartz Volume 7 of Mathematics, Pure, Applied Volume 7 of Pure and applied mathematics, ISSN 0079-8185 Volume 7 of Pure and applied mathematics. A series of texts and monographs |
| Authors | Nelson Dunford, Jacob T. Schwartz |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of California |
| Digitized | 26 Jun 2018 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |