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 1983
Then A is a spectral operator of scalar type . PROOF . The argument of the preceding corollary shows that A is a spectral operator . Since  ( s ) has distinct eigenvalues , it is a scalar operator , that is , its radical part is zero ...
Then A is a spectral operator of scalar type . PROOF . The argument of the preceding corollary shows that A is a spectral operator . Since  ( s ) has distinct eigenvalues , it is a scalar operator , that is , its radical part is zero ...
Page 2396
Leto , be as in the preceding lemma , put A ( a ) = Aoli , ula ) ) ) , and let B ( a ) = A ( 04 ( :, u ( a ) ) ) ( cf. Lemma 4 for the definition of u ( a ) ) . Then , by the preceding lemma , by Lemma 1 , and by formulas ( 2a ) and ...
Leto , be as in the preceding lemma , put A ( a ) = Aoli , ula ) ) ) , and let B ( a ) = A ( 04 ( :, u ( a ) ) ) ( cf. Lemma 4 for the definition of u ( a ) ) . Then , by the preceding lemma , by Lemma 1 , and by formulas ( 2a ) and ...
Page 2455
Therefore , if we let the three operators of the preceding lemma be H2 , H1 , H1 , we obtain the present corollary . Q.E.D. 5 COROLLARY . Under the hypotheses of the preceding corollary , U ( H , H , ) is an isometric mapping of < ( H1 ...
Therefore , if we let the three operators of the preceding lemma be H2 , H1 , H1 , we obtain the present corollary . Q.E.D. 5 COROLLARY . Under the hypotheses of the preceding corollary , U ( H , H , ) is an isometric mapping of < ( H1 ...
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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 fact 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 |