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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 both
...
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 both
...
Page 728
treatment was given by Phillips [ 5 ] . Bade [ 1 ] showed that for the infinitesimal
generator of a group , it is possible to extend the class of functions to include
polynomials and other functions with similar growth conditions . The treatment in
...
treatment was given by Phillips [ 5 ] . Bade [ 1 ] showed that for the infinitesimal
generator of a group , it is possible to extend the class of functions to include
polynomials and other functions with similar growth conditions . The treatment in
...
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 adjoint , was given by ...
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 adjoint , was given by ...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
80 other sections not shown
Common terms and phrases
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 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
References to this book
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 Wiley classics library |
| Authors | Nelson Dunford, Jacob T. Schwartz, William G. Bade |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of Michigan |
| Digitized | 20 Nov 2007 |
| ISBN | 0470226056, 9780470226056 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |