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 75
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 .
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 .
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 ( a ; T ) is compact for every 10 ( T ) ; λ ( c ) every do in o ( T ) is a pole of finite order vede ) of the ...
If T is discrete , then ( a ) its spectrum is a denumerable set of points with no finite limit point ; ( b ) the resolvent R ( a ; T ) is compact for every 10 ( T ) ; λ ( c ) every do in o ( T ) is a pole of finite order vede ) of the ...
Page 2469
Therefore , for each n ε 21 and each € > 0 , the operator Vn.e ) is very smooth and finite . If we now choose n = n ( e ) so that IV ( n ) – V * < € / 2 , then choose d = 8 ( e ) so that IV ( 1.0 ) – V ( n ) / * < 8/2 , and put y ( 6 ) ...
Therefore , for each n ε 21 and each € > 0 , the operator Vn.e ) is very smooth and finite . If we now choose n = n ( e ) so that IV ( n ) – V * < € / 2 , then choose d = 8 ( e ) so that IV ( 1.0 ) – V ( n ) / * < 8/2 , and put y ( 6 ) ...
What people are saying - Write a review
We haven't found any reviews in the usual places.
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
47 other sections not shown
Other editions - View all
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 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 |