Linear Operators: General theory |
From inside the book
Results 1-3 of 65
Page 168
Let ( S , E , u ) be a positive measure space and G a separable subset of L , ( S ,
E , u , X ) , where 1 sp < 0o . Then there is a set S , in E , a sub o - field & of E ( S )
, and a closed separable subspace X , of 2 such that the restriction My of u to Ey ...
Let ( S , E , u ) be a positive measure space and G a separable subset of L , ( S ,
E , u , X ) , where 1 sp < 0o . Then there is a set S , in E , a sub o - field & of E ( S )
, and a closed separable subspace X , of 2 such that the restriction My of u to Ey ...
Page 426
1 THEOREM . If X is a B - space , then the X topology of the closed unit sphere S
* of X * is a metric topology if and only if X is separable . PROOF . If X is
separable , let { wn } be a countable dense subset of X , and define 1 | ( ~ * — y *
) xml ...
1 THEOREM . If X is a B - space , then the X topology of the closed unit sphere S
* of X * is a metric topology if and only if X is separable . PROOF . If X is
separable , let { wn } be a countable dense subset of X , and define 1 | ( ~ * — y *
) xml ...
Page 504
Theorem 6 remains valid if the hypothesis that X * is the conjugate space of a
separable space is replaced by the hypothesis that X * is the conjugate space of
an arbitrary B - space and T has a separable range . The proof of the corollary
will ...
Theorem 6 remains valid if the hypothesis that X * is the conjugate space of a
separable space is replaced by the hypothesis that X * is the conjugate space of
an arbitrary B - space and T has a separable range . The proof of the corollary
will ...
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 |
Algebraic Preliminaries | 34 |
Copyright | |
31 other sections not shown
Other editions - View all
Common terms and phrases
algebra Amer analytic applied arbitrary assumed B-space Banach spaces bounded called clear closed compact operator complex condition Consequently constant contains continuous functions converges convex convex set Corollary countably additive defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hence Hilbert space identity implies inequality integral interval Lebesgue Lemma limit linear functional linear operator linear space Math neighborhood norm operator operator topology problem projection PROOF properties proved range reflexive representation respect 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
Bibliographic information
| Title | Linear Operators: General theory Volume 1 of Linear Operators, Jacob T. Schwartz Volume 7 of Pure and applied mathematics |
| Author | Nelson Dunford |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of California |
| Digitized | 16 Mar 2011 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |