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 88
Page 1953
PROOF . If either AT = 0 or TA = 0 then , by the theorem , either A = AE ( { 0 } ) or A = E ( { 0 } ) A . Thus A = 0 . Q.E.D. 12 COROLLARY . If E ( { a } ) = 0 , then ( 21 – T ' ) X is dense in X. Proof . First suppose that = 0 .
PROOF . If either AT = 0 or TA = 0 then , by the theorem , either A = AE ( { 0 } ) or A = E ( { 0 } ) A . Thus A = 0 . Q.E.D. 12 COROLLARY . If E ( { a } ) = 0 , then ( 21 – T ' ) X is dense in X. Proof . First suppose that = 0 .
Page 2137
Even though ( A ) is taken as a standing assumption throughout this section , it will be indicated parenthetically in the statement of each lemma in the proof of which it is used . 1 LEMMA ( A ) . If a , ß are complex numbers and x ...
Even though ( A ) is taken as a standing assumption throughout this section , it will be indicated parenthetically in the statement of each lemma in the proof of which it is used . 1 LEMMA ( A ) . If a , ß are complex numbers and x ...
Page 2192
This shows that o ( S ( f ) ) 2f ( o ) 2 n f ( 8 ) E ( ) = 1 and completes the proof of the lemma , Q.E.D. 12 COROLLARY . Let A be an algebra of operators in a weakly complete B - space X. Suppose that A is topologically and ...
This shows that o ( S ( f ) ) 2f ( o ) 2 n f ( 8 ) E ( ) = 1 and completes the proof of the lemma , Q.E.D. 12 COROLLARY . Let A be an algebra of operators in a weakly complete B - space X. Suppose that A is topologically and ...
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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 |