Linear Operators, Part 1 |
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Page 419
Nelson Dunford, Jacob T. Schwartz. 2 DEFINITION . Let X be a linear vector
space , and let I be a total subspace of X * . Then the l ' topology of X is the
topology obtained by taking as base all sets of the form N ( p ; A , 8 ) = { 9 ||| ( p ) -
[ ( 9 ) < € ...
Nelson Dunford, Jacob T. Schwartz. 2 DEFINITION . Let X be a linear vector
space , and let I be a total subspace of X * . Then the l ' topology of X is the
topology obtained by taking as base all sets of the form N ( p ; A , 8 ) = { 9 ||| ( p ) -
[ ( 9 ) < € ...
Page 420
Nelson Dunford, Jacob T. Schwartz. in the X * topology if and only if lim , xe = x
weakly in the sense of Definition II.3.25 . On the other hand , if X is a subspace of
y * , then each element y e Y determines the linear functional f , on X defined by 1
...
Nelson Dunford, Jacob T. Schwartz. in the X * topology if and only if lim , xe = x
weakly in the sense of Definition II.3.25 . On the other hand , if X is a subspace of
y * , then each element y e Y determines the linear functional f , on X defined by 1
...
Page 477
strong , and the weak operator topologies in B ( X , Y ) . It is evident that the
uniform operator topology is stronger than the strong operator topology , and that
the strong operator topology is stronger than the weak operator topology . With its
...
strong , and the weak operator topologies in B ( X , Y ) . It is evident that the
uniform operator topology is stronger than the strong operator topology , and that
the strong operator topology is stronger than the weak operator topology . With its
...
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Contents
Preliminary Concepts | 1 |
The VitaliHahnSaks Theorem and Spaces of Measures | 7 |
B Topological Preliminaries | 10 |
Copyright | |
87 other sections not shown
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Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed complex Consequently contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero
Bibliographic information
| Title | Linear Operators, Part 1 Linear Operators, Jacob T. Schwartz Volume 7 of Mathematics, Pure, Applied Volume 7 of Pure and applied mathematics, ISSN 0079-8185 Volume 7 of Pure and applied mathematics. A series of texts and monographs |
| Authors | Nelson Dunford, Jacob T. Schwartz |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of California |
| Digitized | 26 Jun 2018 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |