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 2257
01 point in o ( R ) , including zero , is contained in an arbitrarily small compact set open in the relative topology of o ( R ) . Hence , o ( R ) is totally disconnected . It follows by Definition VII.9.3 that Elo ; T ) = E ( 70 ) ...
01 point in o ( R ) , including zero , is contained in an arbitrarily small compact set open in the relative topology of o ( R ) . Hence , o ( R ) is totally disconnected . It follows by Definition VII.9.3 that Elo ; T ) = E ( 70 ) ...
Page 2360
It will also be shown that T- " is compact . From this , ( iii ) , and Theorem VI.5.4 , it will follow that B ( u ) = R ( M ; T + P ) is compact for u in V , and i sufficiently large , so that the theorem will be proved .
It will also be shown that T- " is compact . From this , ( iii ) , and Theorem VI.5.4 , it will follow that B ( u ) = R ( M ; T + P ) is compact for u in V , and i sufficiently large , so that the theorem will be proved .
Page 2462
is compact . Put C = QR1 , and D R2 , so that V = CD . The operator C is compact by Corollary V1.5.5 , and thus proof of Corollary 11 is complete . Q.E.D. 12 LEMMA . If C is a compact operator in H , and { T , } is a uniformly bounded ...
is compact . Put C = QR1 , and D R2 , so that V = CD . The operator C is compact by Corollary V1.5.5 , and thus proof of Corollary 11 is complete . Q.E.D. 12 LEMMA . If C is a compact operator in H , and { T , } is a uniformly bounded ...
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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 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 |