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Page 239
It consists of ordered n - tuples x = [ Q2 , ... , Com ] of scalars Qj , ... , On and has the norm n lac ] = { Elain } 110 . { Σ | α . 3. The space Inc is the linear space of all ordered n - tuples [ cy , . .. , Cen ] of scalars Oy ...
It consists of ordered n - tuples x = [ Q2 , ... , Com ] of scalars Qj , ... , On and has the norm n lac ] = { Elain } 110 . { Σ | α . 3. The space Inc is the linear space of all ordered n - tuples [ cy , . .. , Cen ] of scalars Oy ...
Page 472
168 ] showed that the norm in C [ 0 , 1 ] is strongly differentiable at x , € C [ 0 , 1 ] if and only if the function X , achieves its maximum at exactly one point . Mazur ( 1 ; p . 78–79 ] proved that the same condition holds in B ( S ) ...
168 ] showed that the norm in C [ 0 , 1 ] is strongly differentiable at x , € C [ 0 , 1 ] if and only if the function X , achieves its maximum at exactly one point . Mazur ( 1 ; p . 78–79 ] proved that the same condition holds in B ( S ) ...
Page 532
21 Show that the map T defined by 1 ( a ) ( Hardy ) ( Tf ) ( x ) = - Styldy dy is a map in Ly ( 0 , 0 ) of norm p / ( p - 1 ) , p > 1 , ( b ) ( Hilbert , Schur , Hardy , M. Riesz ) fly ) ( 7 0 x + y is a map in L , ( 0 , 0 ) of norm r ...
21 Show that the map T defined by 1 ( a ) ( Hardy ) ( Tf ) ( x ) = - Styldy dy is a map in Ly ( 0 , 0 ) of norm p / ( p - 1 ) , p > 1 , ( b ) ( Hilbert , Schur , Hardy , M. Riesz ) fly ) ( 7 0 x + y is a map in L , ( 0 , 0 ) of norm r ...
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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