Linear Operators: General theory |
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Page 376
... 6.12 , 6.31 13.13 13.14 6.31 6.31 Y Convergence in X = y * meaningless meaning less meaning . less 13.13 13.14 Miscellaneous Properties 13.13 ( F4 ) 13.14 ( F4 ) 6.18 6.19 ( F4 ) 13.76 6.18 6.19 ( F4 ) 6.16 , 6.17 , 6.26 V.8.8 ( F4 ) ...
... 6.12 , 6.31 13.13 13.14 6.31 6.31 Y Convergence in X = y * meaningless meaning less meaning . less 13.13 13.14 Miscellaneous Properties 13.13 ( F4 ) 13.14 ( F4 ) 6.18 6.19 ( F4 ) 13.76 6.18 6.19 ( F4 ) 6.16 , 6.17 , 6.26 V.8.8 ( F4 ) ...
Page 534
L. ( S , E , u ) has a known meaning ; in the course of this section we will also see how to define L ( S , E , u ) . For 1 Spoo , L , is a B - space , but for 0 < p < 1 , L , is merely an F - space ( cf.
L. ( S , E , u ) has a known meaning ; in the course of this section we will also see how to define L ( S , E , u ) . For 1 Spoo , L , is a B - space , but for 0 < p < 1 , L , is merely an F - space ( cf.
Page 684
... 0 St } of bounded linear operators in a B - space X for which ( i ) T ( 0 ) = I , T ( t + u ) = T ( t ) T ( u ) , In order to be able to assign a meaning to. 0 < t , u . n - 00 0 < x < 0 684 VIII.7 VIII .
... 0 St } of bounded linear operators in a B - space X for which ( i ) T ( 0 ) = I , T ( t + u ) = T ( t ) T ( u ) , In order to be able to assign a meaning to. 0 < t , u . n - 00 0 < x < 0 684 VIII.7 VIII .
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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