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 |
From inside the book
Results 1-3 of 79
Page 2357
2 , each of these finite sums has a finite dimensional range and is hence compact
, it follows from Lemma V1 . 5 . 3 that for v > 0 the operator ( T - 101 ) - v is
compact . Thus , if v > 0 , then since P + T = ( P + 101 ) + ( T - 107 ) , and since ( P
+ do ...
2 , each of these finite sums has a finite dimensional range and is hence compact
, it follows from Lemma V1 . 5 . 3 that for v > 0 the operator ( T - 101 ) - v is
compact . Thus , if v > 0 , then since P + T = ( P + 101 ) + ( T - 107 ) , and since ( P
+ do ...
Page 2360
It will also be shown that T - v is compact . From this , ( iii ) , and Theorem VI . 5 . 4
, it will follow that B ( u ) = R ( u ; T + P ) is compact for u in V , and i sufficiently
large , so that the theorem will be proved . Let u be in V . To show that \ T ' ' R ( u ...
It will also be shown that T - v is compact . From this , ( iii ) , and Theorem VI . 5 . 4
, it will follow that B ( u ) = R ( u ; T + P ) is compact for u in V , and i sufficiently
large , so that the theorem will be proved . Let u be in V . To show that \ T ' ' R ( u ...
Page 2462
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 { Tn } is a
uniformly bounded sequence of operators in H converging strongly to zero ...
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 { Tn } is a
uniformly bounded sequence of operators in H converging strongly to zero ...
What people are saying - Write a review
We haven't found any reviews in the usual places.
Contents
SPECTRAL OPERATORS XV Spectral Operators | 1924 |
Introduction | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
32 other sections not shown
Other editions - View all
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 |