Linear Operators: General theory |
From inside the book
Results 1-3 of 88
Page 19
The metric topology in X is the smallest topology containing the spheres . The set X , with its metric topology , is called a metric space . If X is a topological space such that there exists a metric function whose topology is the same ...
The metric topology in X is the smallest topology containing the spheres . The set X , with its metric topology , is called a metric space . If X is a topological space such that there exists a metric function whose topology is the same ...
Page 20
A sequence { an } in a metric space is a Cauchy sequence if limn . o ( am , an ) = 0. If every Cauchy sequence is convergent , a metric space is said to be complete . The next three lemmas are immediate consequences of the definitions .
A sequence { an } in a metric space is a Cauchy sequence if limn . o ( am , an ) = 0. If every Cauchy sequence is convergent , a metric space is said to be complete . The next three lemmas are immediate consequences of the definitions .
Page 91
admits an equivalent metric under which it is complete , then G admits an invariant metric and is complete under each invariant metric . Thus every complete linear metric space can be metrized to be an F - space .
admits an equivalent metric under which it is complete , then G admits an invariant metric and is complete under each invariant metric . Thus every complete linear metric space can be metrized to be an F - space .
What people are saying - Write a review
Reviews aren't verified, but Google checks for and removes fake content when it's identified
User Review - Flag as inappropriate
i want to read
Contents
B Topological Preliminaries | 10 |
quences | 26 |
Algebraic Preliminaries | 34 |
Copyright | |
80 other sections not shown
Other editions - View all
Common terms and phrases
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