Linear Operators: General theory |
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Page 387
A detailed proof was given by Fréchet [ 5 ; III . p . 441 ] . The theorem for L , [ 0 , 1 ] , 1 < p < 0o , was demonstrated by F. Riesz [ 2 ; p . 475 ] . In the case of a finite measure space the theorem was established by Nikodým [ 9 ...
A detailed proof was given by Fréchet [ 5 ; III . p . 441 ] . The theorem for L , [ 0 , 1 ] , 1 < p < 0o , was demonstrated by F. Riesz [ 2 ; p . 475 ] . In the case of a finite measure space the theorem was established by Nikodým [ 9 ...
Page 392
tion with respect to a vector valued measure which is presented here is the one given in Bartle , Dunford and Schwartz [ 1 ] . A similar procedure has been employed by Bartle [ 3 ] to obtain a Lebesgue - type integration theory where ...
tion with respect to a vector valued measure which is presented here is the one given in Bartle , Dunford and Schwartz [ 1 ] . A similar procedure has been employed by Bartle [ 3 ] to obtain a Lebesgue - type integration theory where ...
Page 729
proofs , valid in uniformly convex spaces , were given by G. Birkhoff [ 7 ] and F. Riesz [ 16 , 18 ] . Another proof , based on the interesting fact that a fixed point for a contraction in Hilbert space is also a fixed point for its ...
proofs , valid in uniformly convex spaces , were given by G. Birkhoff [ 7 ] and F. Riesz [ 16 , 18 ] . Another proof , based on the interesting fact that a fixed point for a contraction in Hilbert space is also a fixed point for its ...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
quences | 26 |
Copyright | |
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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 1 of Linear Operators: General Theory. Spectral Theory, Self Adjoint Operators in Hilbert Space. Spectral Operators. I. II. III, William George Bade Volume 7 of Pure & Applied Mathematics : a Wiley-interscience series of texts, monographs & tracts 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 Wiley classics library |
| Authors | Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle |
| Editors | William G. Bade, Robert G. Bartle |
| Contributor | Karreman Mathematics Research Collection |
| Edition | reprint |
| 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 |