Linear Operators: General theory |
From inside the book
Results 1-3 of 90
Page 263
Since G is an arbitrary open set containing F1 - G , we have My ( F1 ) S2 ( G ) +41 ( F1 - G7 ) . If F is a closed set it follows from this inequality , by allowing G , to range over all open sets containing FF , that # 1 ( F ) < !
Since G is an arbitrary open set containing F1 - G , we have My ( F1 ) S2 ( G ) +41 ( F1 - G7 ) . If F is a closed set it follows from this inequality , by allowing G , to range over all open sets containing FF , that # 1 ( F ) < !
Page 432
is an arbitrary finite subset of X * , then there exists a ze À such that ***** = *** , i = 1 , ... , n . To see this , let m be an arbitrary integer ; since x ** is in the X * -closure of x ( A ) , there is an element zm € A such that ...
is an arbitrary finite subset of X * , then there exists a ze À such that ***** = *** , i = 1 , ... , n . To see this , let m be an arbitrary integer ; since x ** is in the X * -closure of x ( A ) , there is an element zm € A such that ...
Page 476
N ( T ; A , E ) = { RR € B ( X , Y ) , ( T - R ) .x < E , & € A } where A is an arbitrary finite subset of X , and e > 0 is arbitrary . Thus , in the strong topology , a generalized sequence { Tx } converges to T if and only if { Tqx } ...
N ( T ; A , E ) = { RR € B ( X , Y ) , ( T - R ) .x < E , & € A } where A is an arbitrary finite subset of X , and e > 0 is arbitrary . Thus , in the strong topology , a generalized sequence { Tx } converges to T if and only if { Tqx } ...
What people are saying - Write a review
We haven't found any reviews in the usual places.
Contents
Preliminary Concepts | 1 |
The VitaliHahnSaks Theorem and Spaces of Measures | 7 |
B Topological Preliminaries | 10 |
Copyright | |
91 other sections not shown
Other editions - View all
Common terms and phrases
Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed closure complex condition Consequently contains continuous functions converges Corollary defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows formula function f given Hence Hilbert space implies integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space linear topological space Math means measure space metric space neighborhood norm open set operator problem Proc projection Proof properties proved range reflexive respect Russian satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero