Linear Operators: General theory |
From inside the book
Results 1-3 of 48
Page 26
Thus S ( x , 2 - K ) CUm , which shows that the identity mapping of X with the metric topology onto X with the given topology is continuous . Hence the identity is a homeomorphism and the space is metrizable . Q.E.D. W - y 7.
Thus S ( x , 2 - K ) CUm , which shows that the identity mapping of X with the metric topology onto X with the given topology is continuous . Hence the identity is a homeomorphism and the space is metrizable . Q.E.D. W - y 7.
Page 479
When these inverses exist , ( T - 1 ) * ( T * ) - 1 . PROOF . If T - 1 exists and is in B ( Y , X ) , then , by Lemma 4 , ( TT - 1 ) * ( T - 1 ) * T * is the identity in Y * and ( T - 1T ) * = T * ( T - 1 ) ...
When these inverses exist , ( T - 1 ) * ( T * ) - 1 . PROOF . If T - 1 exists and is in B ( Y , X ) , then , by Lemma 4 , ( TT - 1 ) * ( T - 1 ) * T * is the identity in Y * and ( T - 1T ) * = T * ( T - 1 ) ...
Page 661
The identity ' - 1 Tn n - 1 ( * ) A ( n ) A ( n - 1 ) n n shows that { T " / n } is bounded and hence , by II.1.18 , the set of x for which Trę / n +0 is a closed linear manifold . Thus X , is a closed linear manifold and , since a ...
The identity ' - 1 Tn n - 1 ( * ) A ( n ) A ( n - 1 ) n n shows that { T " / n } is bounded and hence , by II.1.18 , the set of x for which Trę / n +0 is a closed linear manifold . Thus X , is a closed linear manifold and , since a ...
What people are saying - Write a review
User Review - Flag as inappropriate
i want to read
Contents
B Topological Preliminaries | 10 |
quences | 26 |
Algebraic Preliminaries | 34 |
Copyright | |
80 other sections not shown
Other editions - View all
Common terms and phrases
Acad 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 semi-group 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