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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 .
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 .
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 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 ) .
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 .
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 .
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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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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 | 26 Jun 2018 |
| ISBN | 0470226056, 9780470226056 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |