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 2174
In a Hilbert space the condition that lett | S M for all t e R implies that T is
equivalent to a self adjoint operator and hence is a scalar type operator with real
spectrum . ( This follows from Lemma XV . 6 . 1 which implies that the bounded
group G ...
In a Hilbert space the condition that lett | S M for all t e R implies that T is
equivalent to a self adjoint operator and hence is a scalar type operator with real
spectrum . ( This follows from Lemma XV . 6 . 1 which implies that the bounded
group G ...
Page 2295
Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the
Assistance of William G. Bade and Robert G. Bartle Nelson Dunford, Jacob T.
Schwartz, William G. Bade, Robert G. Bartle L. Bers, J. J. Stoker. Hence fu ( T ) E (
; T ...
Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the
Assistance of William G. Bade and Robert G. Bartle Nelson Dunford, Jacob T.
Schwartz, William G. Bade, Robert G. Bartle L. Bers, J. J. Stoker. Hence fu ( T ) E (
; T ...
Page 2357
then it is clear that L is a bounded operator and that ( 8 – XI ) v = ( T – XI ) - ' L .
Hence ( P + N ) ( 8 – XI ) - ° = P ( S – XI ) - ° + N ( S — 2 / ) - = P ( T – XI ) - " L + N (
S – XI ) - v is a bounded operator which is compact if P ( T - 21 ) - is compact ( cf .
then it is clear that L is a bounded operator and that ( 8 – XI ) v = ( T – XI ) - ' L .
Hence ( P + N ) ( 8 – XI ) - ° = P ( S – XI ) - ° + N ( S — 2 / ) - = P ( T – XI ) - " L + N (
S – XI ) - v is a bounded operator which is compact if P ( T - 21 ) - is compact ( cf .
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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 |