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 2283
Then a projection E in B has finite uniform multiplicity n if and only if its adjoint E *
in B * has finite uniform multiplicity n . PROOF . It is sufficient to suppose E and E
* satisfy the countable chain condition . Also since each projection is the union ...
Then a projection E in B has finite uniform multiplicity n if and only if its adjoint E *
in B * has finite uniform multiplicity n . PROOF . It is sufficient to suppose E and E
* satisfy the countable chain condition . Also since each projection is the union ...
Page 2292
If T is discrete , then ( a ) its spectrum is a denumerable set of points with no finite
limit point ; ( b ) the resolvent R ( 2 ; T ) is compact for every 1 € ( T ) ; ( c ) every
do in o ( T ) is a pole of finite order vido ) of the resolvent and if , for some positive
...
If T is discrete , then ( a ) its spectrum is a denumerable set of points with no finite
limit point ; ( b ) the resolvent R ( 2 ; T ) is compact for every 1 € ( T ) ; ( c ) every
do in o ( T ) is a pole of finite order vido ) of the resolvent and if , for some positive
...
Page 2469
Therefore , for each n 2 1 and each & > 0 , the operator Vin , e ) is very smooth
and finite . If we now choose n = n ( e ) so that IV ( n ) — V ] * < 8/2 , then choose d
= d ( 8 ) so that Vin . ( no ) - V « / * < 8/2 , and put y ( ) = V 4,0 ) -V , it follows that V
...
Therefore , for each n 2 1 and each & > 0 , the operator Vin , e ) is very smooth
and finite . If we now choose n = n ( e ) so that IV ( n ) — V ] * < 8/2 , then choose d
= d ( 8 ) so that Vin . ( no ) - V « / * < 8/2 , and put y ( ) = V 4,0 ) -V , it follows that V
...
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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 |