Linear Operators: General theory |
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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 Ey of E ( S
) , and a closed separable subspace X , of 2 such that the restriction My of u to E ...
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 Ey of E ( S
) , and a closed separable subspace X , of 2 such that the restriction My of u to E ...
Page 426
If X is separable , let { xn } be a countable dense subset of X , and define 1 | ( x *
—y * ) xm | 8 ( 2 * , y * ) n = 1 21 1 + ( x * -- ** ) x It is easy to verify that the
topology of S * defined by this metric is weaker than the X topology of S * . Hence
, by ...
If X is separable , let { xn } be a countable dense subset of X , and define 1 | ( x *
—y * ) xm | 8 ( 2 * , y * ) n = 1 21 1 + ( x * -- ** ) x It is easy to verify that the
topology of S * defined by this metric is weaker than the X topology of S * . Hence
, by ...
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 ...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
quences | 26 |
Copyright | |
80 other sections not shown
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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
Bibliographic information
| Title | Linear Operators: General theory Part 1 of Linear Operators, Jacob T. Schwartz Volume 7 of Pure and applied mathematics Interscience Press Pure and applied mathematics Wiley classics library |
| Authors | Nelson Dunford, Jacob T. Schwartz |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of California |
| Digitized | 16 Mar 2011 |
| ISBN | 0470226056, 9780470226056 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |