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Page 511
9. Exercises 1 The space B ( x , y ) is algebraically isomorphic to a subspace of the product Pxex Yz , where Ya = y , under the mapping T → PxxTx . Show that the strong topology of operators in B ( X , Y ) is identical with the usual ...
9. Exercises 1 The space B ( x , y ) is algebraically isomorphic to a subspace of the product Pxex Yz , where Ya = y , under the mapping T → PxxTx . Show that the strong topology of operators in B ( X , Y ) is identical with the usual ...
Page 540
operator and the operator mapping into a weakly complete space X. Weakly compact operators from C [ 0 , 1 ] to X were treated by Sirvint ( 3 ] . A very incisive discussion of weakly compact operators with domain C ( S ) was given by ...
operator and the operator mapping into a weakly complete space X. Weakly compact operators from C [ 0 , 1 ] to X were treated by Sirvint ( 3 ] . A very incisive discussion of weakly compact operators with domain C ( S ) was given by ...
Page 599
11 Let Xy be a closed subspace of a B - space X such that T X , CX for each operator Tn in a sequence { Tn , n = 1 , 2 , ... } of commuting operators in B ( X ) . Let U , be the restriction of T , to X and let Vn : X / X1 + X / X ...
11 Let Xy be a closed subspace of a B - space X such that T X , CX for each operator Tn in a sequence { Tn , n = 1 , 2 , ... } of commuting operators in B ( X ) . Let U , be the restriction of T , to X and let Vn : X / X1 + X / X ...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
quences | 26 |
Copyright | |
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Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero