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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Results 1-3 of 87
Page 1955
We shall be concerned with the fine structure of the spectrum , and the spectral
points of an operator in X will be classified , as they were in Hilbert space ,
according to the following definition . + 1 DEFINITION . Let A be a bounded linear
...
We shall be concerned with the fine structure of the spectrum , and the spectral
points of an operator in X will be classified , as they were in Hilbert space ,
according to the following definition . + 1 DEFINITION . Let A be a bounded linear
...
Page 1957
Thus , by the preceding corollary , we have O ( S ) Şo ( To ) , and so to prove the
present corollary , it suffices to prove that is in the continuous spectrum of S . . Let
( S – 11 ) x = 0 , where x is in E ( 0 ) X . Since S and T have the same resolution ...
Thus , by the preceding corollary , we have O ( S ) Şo ( To ) , and so to prove the
present corollary , it suffices to prove that is in the continuous spectrum of S . . Let
( S – 11 ) x = 0 , where x is in E ( 0 ) X . Since S and T have the same resolution ...
Page 2591
2 (1930) Spectral set for an operator, XV.2 (1930) Spectrum, of a spectral
operator, XV.8 (1954) condition to be in point spectrum, XV.15.13 (2076)
continuous spectrum, definition of, XV.8.1 (1955) examples of, XV.15.37, XV.
15.38, XV. 15.
2 (1930) Spectral set for an operator, XV.2 (1930) Spectrum, of a spectral
operator, XV.8 (1954) condition to be in point spectrum, XV.15.13 (2076)
continuous spectrum, definition of, XV.8.1 (1955) examples of, XV.15.37, XV.
15.38, XV. 15.
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Contents
SPECTRAL OPERATORS XV Spectral Operators | 1924 |
Introduction | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
32 other sections not shown
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Common terms and phrases
analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear clearly closure commuting compact complex consider constant contained converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established example exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum statement strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly 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 |