Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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Page 2397
The theorem will follow as soon as it is shown that the hypotheses of Theorem XVIII.2.34 are satisfied . In the notation of that theorem o ( T ) ... Hypothesis ( i ) of Theorem XVIII.2.34 is satisfied by virtue of Corollaries 9 and 11.
The theorem will follow as soon as it is shown that the hypotheses of Theorem XVIII.2.34 are satisfied . In the notation of that theorem o ( T ) ... Hypothesis ( i ) of Theorem XVIII.2.34 is satisfied by virtue of Corollaries 9 and 11.
Page 2401
Using hypothesis ( c ) , we may write this last equation as ( 5 ) q ( B - ( B , A ; ) ) = 9 ( A1 ) . Now , by hypothesis , the map B ~ ( B , Ay ) of A → A has norm at most M2 ( M + ...
Using hypothesis ( c ) , we may write this last equation as ( 5 ) q ( B - ( B , A ; ) ) = 9 ( A1 ) . Now , by hypothesis , the map B ~ ( B , Ay ) of A → A has norm at most M2 ( M + ...
Page 2449
By hypotheses ( d ) and ( e ) , this last equation would follow from ( 4 ) A + 4 ( A , A ) - A , A1 ) = A1 ; thus , to solve ( 1 ) , we have only to ... Since , by hypothesis , 6 Mt 31 , we have In + 1 < 2t , and our assertion follows .
By hypotheses ( d ) and ( e ) , this last equation would follow from ( 4 ) A + 4 ( A , A ) - A , A1 ) = A1 ; thus , to solve ( 1 ) , we have only to ... Since , by hypothesis , 6 Mt 31 , we have In + 1 < 2t , and our assertion follows .
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
47 other sections not shown
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adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero
Bibliographic information
| Title | Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 Pure and applied mathematics, v. 7 |
| Authors | Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle |
| Editors | L. Bers, J. J. Stoker |
| Publisher | Wiley-Interscience, 1957 |
| Original from | the University of Michigan |
| Digitized | 2 Feb 2010 |
| ISBN | 0471226394, 9780471226390 |
| Length | 667 pages |
| Export Citation | BiBTeX EndNote RefMan |