Linear Operators: General theory |
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Page 373
44 ] and for integrals by F . Riesz [ 2 ; p . 456 ] . Lemma 4 . 2 is due to F . Riesz [ 8
; p . 36 ] and was also used by Sz . - Nagy [ 5 ] . A similar argument may be
applied to obtain this result in any uniformly convex B - space . This generalizes
and ...
44 ] and for integrals by F . Riesz [ 2 ; p . 456 ] . Lemma 4 . 2 is due to F . Riesz [ 8
; p . 36 ] and was also used by Sz . - Nagy [ 5 ] . A similar argument may be
applied to obtain this result in any uniformly convex B - space . This generalizes
and ...
Page 388
1363 ] and F . Riesz [ 13 ] . THEOREM . If 1 < p < oo then a sequence { In }
converges strongly to | in L ( S , E , u ) if and only if it converges weakly and in i .
This theorem remains valid in any uniformly convex B - space . Theorem 8 . 15
was ...
1363 ] and F . Riesz [ 13 ] . THEOREM . If 1 < p < oo then a sequence { In }
converges strongly to | in L ( S , E , u ) if and only if it converges weakly and in i .
This theorem remains valid in any uniformly convex B - space . Theorem 8 . 15
was ...
Page 608
However , it seems fair to state that it was F . Riesz who most fully revealed and
developed it along the lines presented here . The reader of his book ( F . Riesz (
3 ) , particularly Secs . 71 - 82 ) will find many of these concepts and results ...
However , it seems fair to state that it was F . Riesz who most fully revealed and
developed it along the lines presented here . The reader of his book ( F . Riesz (
3 ) , particularly Secs . 71 - 82 ) will find many of these concepts and results ...
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Contents
Preliminary Concepts A Settheoretic Preliminaries 1 Notation and Elementary Notions | 1 |
Partially Ordered Systems | 7 |
Exercises | 9 |
Copyright | |
35 other sections not shown
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Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |
Common terms and phrases
algebra analytic applied arbitrary assumed B-space ba(S Borel bounded called Chapter clear closed compact complex condition Consequently constant contains continuous functions converges Corollary countably additive defined DEFINITION denote dense determined differential dimensional disjoint element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hausdorff Hence Hilbert space identity implies inequality integral interval isometric isomorphism Lebesgue Lemma limit linear functional linear space mapping Math means measure space neighborhood norm obtained operator positive measure preceding projection PROOF properties proved range reflexive regular respect satisfies scalar seen separable sequence sequentially set function Show shown statement subset subspace sufficient Suppose Theorem theory tion topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero
Bibliographic information
| Title | Linear Operators: General theory Part 1 of Linear Operators, Jacob T. Schwartz Volume 1; Volume 7 of Pure and applied mathematics : a series of texts and monographs Volume 7 of Pure and applied mathematics Interscience Press Pure and applied mathematics, ISSN 0079-8185 |
| Authors | Nelson Dunford, Jacob T. Schwartz |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of Michigan |
| Digitized | 20 Nov 2007 |
| Length | 2592 pages |
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