Linear Operators: General theory |
From inside the book
Results 1-3 of 75
Page 151
Consequently , sup || n Imlo Slim sup ( SF , \ n ( 8 ) –Im ( 8 ) pulp , ds ) } " + 2ello Slim sup [ { SE . \\ . ( 8 ) –f ( s ) pulu , ds ) " " " + { SE . \ tm ( 8 ) – † ( 8 ) | ” 0 ( ja , ds ) " ' ] + 2ello 2ɛllo , so that lim in - Iml ...
Consequently , sup || n Imlo Slim sup ( SF , \ n ( 8 ) –Im ( 8 ) pulp , ds ) } " + 2ello Slim sup [ { SE . \\ . ( 8 ) –f ( s ) pulu , ds ) " " " + { SE . \ tm ( 8 ) – † ( 8 ) | ” 0 ( ja , ds ) " ' ] + 2ello 2ɛllo , so that lim in - Iml ...
Page 451
Since the function 1 g ( a , x , y ) { t ( x + ay ) -2 ( x ) + ( x - ay ) } a 2n , i , i { is ( by Lemma 1 ) the sum of two monotone increasing functions of a it has this same property for all x , y € X. Consequently , letting = x \ x ...
Since the function 1 g ( a , x , y ) { t ( x + ay ) -2 ( x ) + ( x - ay ) } a 2n , i , i { is ( by Lemma 1 ) the sum of two monotone increasing functions of a it has this same property for all x , y € X. Consequently , letting = x \ x ...
Page 627
Consequently , by the Weierstrass approximation theorem , and Corollary III.10.6 , So hlu ) g ( u ) du = S'h ( u ) G ( du ) , he C ( 0 , 1 ) , where G ( E ) = Seg ( u ) du . Since Lebesgue measure is regular so is G and thus , by the ...
Consequently , by the Weierstrass approximation theorem , and Corollary III.10.6 , So hlu ) g ( u ) du = S'h ( u ) G ( du ) , he C ( 0 , 1 ) , where G ( E ) = Seg ( u ) du . Since Lebesgue measure is regular so is G and thus , by the ...
What people are saying - Write a review
We haven't found any reviews in the usual places.
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
quences | 26 |
Copyright | |
80 other sections not shown
Other editions - View all
Common terms and phrases
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