Linear Operators, Part 1 |
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Page 403
It follows from the rotational invariance of un that Un may be regarded as a
measure defined intrinsically in any n - dimensional real Hilbert space H , without
reference to any particular coordinate system in that space . This measure will be
...
It follows from the rotational invariance of un that Un may be regarded as a
measure defined intrinsically in any n - dimensional real Hilbert space H , without
reference to any particular coordinate system in that space . This measure will be
...
Page 576
It follows from Theorem 10 that the map o → E ( 0 ) is a homeomorphism . To
verify that it is an isomorphism , it will suffice to show that E ( q ) = 0 only when o
is the void set $ . Now if E ( 0 ) = 0 , then X , = { 0 } and o ( T ) . = $ . It follows from
...
It follows from Theorem 10 that the map o → E ( 0 ) is a homeomorphism . To
verify that it is an isomorphism , it will suffice to show that E ( q ) = 0 only when o
is the void set $ . Now if E ( 0 ) = 0 , then X , = { 0 } and o ( T ) . = $ . It follows from
...
Page 689
The desired conclusion follows from Corollary II.3.13 . Q.E.D. 3 COROLLARY . In
a reflexive space , the averages A ( a ) are strongly convergent if they are
bounded and if T ( n ) / n converges to zero strongly . PROOF . This follows from ...
The desired conclusion follows from Corollary II.3.13 . Q.E.D. 3 COROLLARY . In
a reflexive space , the averages A ( a ) are strongly convergent if they are
bounded and if T ( n ) / n converges to zero strongly . PROOF . This follows from ...
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Contents
Preliminary Concepts | 1 |
The VitaliHahnSaks Theorem and Spaces of Measures | 7 |
B Topological Preliminaries | 10 |
Copyright | |
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Common terms and phrases
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 |