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 2013
For a sequence { 0m } satisfying ( 3 ) , A is given by ( 9 ) and the domain of A consists precisely of those o for which the limit in ( 9 ) exists . o Our next concern will be with the question of the existence of a resolution of the ...
For a sequence { 0m } satisfying ( 3 ) , A is given by ( 9 ) and the domain of A consists precisely of those o for which the limit in ( 9 ) exists . o Our next concern will be with the question of the existence of a resolution of the ...
Page 2096
Another characterization of subscalar operators is given , based on a theorem which asserts that , under certain hypotheses , a continuous linear mapping U of a Banach algebra A with unit e into B ( X ) is the projection of a continuous ...
Another characterization of subscalar operators is given , based on a theorem which asserts that , under certain hypotheses , a continuous linear mapping U of a Banach algebra A with unit e into B ( X ) is the projection of a continuous ...
Page 2376
If an unperturbed ” operator T and a “ perturbation ” K are given , one attempts to find an operator U such that T + K = U - TU , in this way reducing the spectral theory of T + K to that of T. We shall see that this idea can be applied ...
If an unperturbed ” operator T and a “ perturbation ” K are given , one attempts to find an operator U such that T + K = U - TU , in this way reducing the spectral theory of T + K to that of T. We shall see that this idea can be applied ...
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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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Common terms and phrases
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 |