Linear Operators, Part 1 |
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Page 410
A set K CX is convex if x , y eK , and 0 sa şi , imply ax + ( 1 - a ) y e K. The
following lemma is an obvious consequence of Definition 1 . 2 LEMMA . The
intersection of an arbitrary family of convex subsets of the linear space X is
convex .
A set K CX is convex if x , y eK , and 0 sa şi , imply ax + ( 1 - a ) y e K. The
following lemma is an obvious consequence of Definition 1 . 2 LEMMA . The
intersection of an arbitrary family of convex subsets of the linear space X is
convex .
Page 418
If Ky , K , are disjoint closed , convex subsets of a locally convex linear
topological space X , and if K , is compact , then some non - zero continuous
linear functional on X separates K , and Kg . 12 COROLLARY . I / K is a closed
convex subset ...
If Ky , K , are disjoint closed , convex subsets of a locally convex linear
topological space X , and if K , is compact , then some non - zero continuous
linear functional on X separates K , and Kg . 12 COROLLARY . I / K is a closed
convex subset ...
Page 461
and an arbitrary convex set is possible , provided they are disjoint ( compare
Theorem 2.8 ) . He also proved that a convex set K which is compact in the X *
topology of the normed linear space X , can be separated from an arbitrary
closed ...
and an arbitrary convex set is possible , provided they are disjoint ( compare
Theorem 2.8 ) . He also proved that a convex set K which is compact in the X *
topology of the normed linear space X , can be separated from an arbitrary
closed ...
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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 |