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 79
Page 1953
Then since the range of T is closed , it follows from Corollary 12 that TX = X. By
Lemma 3.1 the operator T is one - to - one . By Theorem II.2.2 , T has a bounded
inverse and hence 0 € p ( T ) = p ( S ) and so SX = X. Next suppose that E ( { 0 } ...
Then since the range of T is closed , it follows from Corollary 12 that TX = X. By
Lemma 3.1 the operator T is one - to - one . By Theorem II.2.2 , T has a bounded
inverse and hence 0 € p ( T ) = p ( S ) and so SX = X. Next suppose that E ( { 0 } ...
Page 1954
Q.E.D. It was shown in the course of the preceding proof that for an operator T
with a closed range the point = 0 is not in the spectrum of the operator V = T | E ( {
0 } ' ) X . Thus for all sufficiently small complex numbers 1 + 0 the operator AI – T ...
Q.E.D. It was shown in the course of the preceding proof that for an operator T
with a closed range the point = 0 is not in the spectrum of the operator V = T | E ( {
0 } ' ) X . Thus for all sufficiently small complex numbers 1 + 0 the operator AI – T ...
Page 2312
The closure of the range of a densely defined linear operator T is the set of all x
such that y * x = 0 whenever T * y * = 0 . ... range of T , and hence for all y in the
closure of the range of T. On the other hand , if y is not in the closure of the range
of ...
The closure of the range of a densely defined linear operator T is the set of all x
such that y * x = 0 whenever T * y * = 0 . ... range of T , and hence for all y in the
closure of the range of T. On the other hand , if y is not in the closure of the range
of ...
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
28 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 countably additive 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 |