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Page 37
pair X , and if T ( x + y ) = Tx + Ty , T ( x ) = aTx for every de 0 and every Y of vectors in the domain of T. Thus a linear transformation on a linear space X is a homomorphism on the additive group X which commutes with the ...
pair X , and if T ( x + y ) = Tx + Ty , T ( x ) = aTx for every de 0 and every Y of vectors in the domain of T. Thus a linear transformation on a linear space X is a homomorphism on the additive group X which commutes with the ...
Page 494
It is clear that the operator T , defined by ( b ) , is a bounded linear operator on C ( S ) to X whose adjoint T * is given by ( d ) . From IV.10.2 we conclude that T * maps the unit sphere of X * into a conditionally weakly compact ...
It is clear that the operator T , defined by ( b ) , is a bounded linear operator on C ( S ) to X whose adjoint T * is given by ( d ) . From IV.10.2 we conclude that T * maps the unit sphere of X * into a conditionally weakly compact ...
Page 838
8 - 12 ( 71 ) remarks on , ( 93 – 94 ) in a linear space . ( See Hamel base ) orthogonal and orthonormal ... 8 ( 223 ) Borel - Stieltjes measure , ( 142 ) Bound , of an operator , II . 3 . 5 ( 60 ) in a partially ordered set , I . 2 .
8 - 12 ( 71 ) remarks on , ( 93 – 94 ) in a linear space . ( See Hamel base ) orthogonal and orthonormal ... 8 ( 223 ) Borel - Stieltjes measure , ( 142 ) Bound , of an operator , II . 3 . 5 ( 60 ) in a partially ordered set , I . 2 .
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
quences | 26 |
Copyright | |
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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