Linear Operators, Part 1 |
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Page 412
The linear functional f separates the subsets M and N of X if and only if it
separates the subsets M - N and { 0 } of X. The proof is elementary , and is left to
the reader . In dealing with subspaces , it is often convenient to make use of the
following ...
The linear functional f separates the subsets M and N of X if and only if it
separates the subsets M - N and { 0 } of X. The proof is elementary , and is left to
the reader . In dealing with subspaces , it is often convenient to make use of the
following ...
Page 418
If p and q are distinct points of a locally convex linear topological space X , there
is a continuous linear functional f ... tz ) have the same continuous linear
functionals , then a convex set is closed in ( X , 7ı ) if and only if it is closed in ( X ,
T2 ) ...
If p and q are distinct points of a locally convex linear topological space X , there
is a continuous linear functional f ... tz ) have the same continuous linear
functionals , then a convex set is closed in ( X , 7ı ) if and only if it is closed in ( X ,
T2 ) ...
Page 421
Let X be a linear space , and let T be a total subspace of X * . Then the linear
functionals on X which are continuous in the I topology are precisely the
functionals in l . The proof of Theorem 9 will be based on the following lemma .
10 LEMMA .
Let X be a linear space , and let T be a total subspace of X * . Then the linear
functionals on X which are continuous in the I topology are precisely the
functionals in l . The proof of Theorem 9 will be based on the following lemma .
10 LEMMA .
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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 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 |