Linear Operators: General theory |
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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 ... T , ) 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 ... T , ) 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 l be a total subspace of X + . Then the linear
functionals on X which are continuous in the r ' topology are precisely the
functionals in T ' . The proof of Theorem 9 will be based on the following lemma .
Let X be a linear space , and let l be a total subspace of X + . Then the linear
functionals on X which are continuous in the r ' topology are precisely the
functionals in T ' . The proof of Theorem 9 will be based on the following lemma .
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
80 other sections not shown
Common terms and phrases
algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad element 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 meaning measure space metric neighborhood norm operator positive measure problem Proc proof properties proved respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero
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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 Wiley classics library |
| Authors | Nelson Dunford, Jacob T. Schwartz, William G. Bade |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of Michigan |
| Digitized | 20 Nov 2007 |
| ISBN | 0470226056, 9780470226056 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |