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Page 439
Extremal Points 1 DEFINITION . Let K be a subset of a real or complex linear
vector space X . A non - void subset A CK is said to be an extremal subset of K if
a proper convex combination ak , + ( 1 - a ) k , 0 < a < 1 , of two points of K is in A
only ...
Extremal Points 1 DEFINITION . Let K be a subset of a real or complex linear
vector space X . A non - void subset A CK is said to be an extremal subset of K if
a proper convex combination ak , + ( 1 - a ) k , 0 < a < 1 , of two points of K is in A
only ...
Page 440
totally ordered subfamily of A , the non - void set n A , is a closed extremal subset
of K which furnishes a lower bound for A 1 . It follows by Zorn ' s lemma that A
contains a minimal element A . Suppose that A , contains two distinct points p and
...
totally ordered subfamily of A , the non - void set n A , is a closed extremal subset
of K which furnishes a lower bound for A 1 . It follows by Zorn ' s lemma that A
contains a minimal element A . Suppose that A , contains two distinct points p and
...
Page 459
12 Let X be a B - space , and let K be a weakly compact convex subset of X .
Show that K has a continuous tangent functional at each point of a dense subset
of its boundary . 13 Let X be a B - space , and let K * be a bounded X - closed
convex ...
12 Let X be a B - space , and let K be a weakly compact convex subset of X .
Show that K has a continuous tangent functional at each point of a dense subset
of its boundary . 13 Let X be a B - space , and let K * be a bounded X - closed
convex ...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
31 other sections not shown
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algebra Amer analytic applied arbitrary assumed B-space Banach spaces bounded called clear closed compact operator complex condition Consequently constant contains continuous functions converges convex convex set Corollary countably additive defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hence Hilbert space identity implies inequality integral interval Lebesgue Lemma limit linear functional linear operator linear space Math neighborhood norm operator operator topology problem projection PROOF properties proved range reflexive representation respect satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero
Bibliographic information
| Title | Linear Operators: General theory Part 1 of Linear Operators, Jacob T. Schwartz Volume 7 of Pure and applied mathematics Interscience Press Pure and applied mathematics Wiley classics library |
| Authors | Nelson Dunford, Jacob T. Schwartz |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of California |
| Digitized | 16 Mar 2011 |
| ISBN | 0470226056, 9780470226056 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |