Linear Operators, Part 1 |
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Page 50
( a ) In a topological group G , any algebraic combination of any number of
variables X1 , ... , Xn is continuous as a map of GX ... XG into G. ( b ) In a linear
topological space X , all linear combinations of any number of scalars Oy , ... ,
Olom , and ...
( a ) In a topological group G , any algebraic combination of any number of
variables X1 , ... , Xn is continuous as a map of GX ... XG into G. ( b ) In a linear
topological space X , all linear combinations of any number of scalars Oy , ... ,
Olom , and ...
Page 413
non - zero linear functional on the complex space X , which separates the sets M
and N. Q.E.D. 2. Linear Topological Spaces In this section , the results of Section
1 are applied to linear topological spaces . Statements 1-6 of this section are ...
non - zero linear functional on the complex space X , which separates the sets M
and N. Q.E.D. 2. Linear Topological Spaces In this section , the results of Section
1 are applied to linear topological spaces . Statements 1-6 of this section are ...
Page 419
If I is a total linear space of linear functionals on X , X is a locally convex linear
topological space in its ' topology . Note that X may already be a linear
topological space , possessing notions of open and closed subsets , continuous
maps , etc.
If I is a total linear space of linear functionals on X , X is a locally convex linear
topological space in its ' topology . Note that X may already be a linear
topological space , possessing notions of open and closed subsets , continuous
maps , etc.
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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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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 |