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 1994
Then , by Theorem 4 , ang F - nx , and since an q converges , we see from the continuity of F that > Х m.no O lim lĂr ( s ) — 1 ( ) 2 ds = 0 , which implies ( III.3.6 ) that Ăn converges in measure on o . Conversely , if ( 29 ) and ( 30 ) ...
Then , by Theorem 4 , ang F - nx , and since an q converges , we see from the continuity of F that > Х m.no O lim lĂr ( s ) — 1 ( ) 2 ds = 0 , which implies ( III.3.6 ) that Ăn converges in measure on o . Conversely , if ( 29 ) and ( 30 ) ...
Page 2218
It must be shown that { E , } converges strongly to E. By Lemma 6 , E is in B and so a consideration of the sequence { E. -E } shows that it may be assumed that E 0. Thus , to make an indirect proof , it is assumed that the sequence ...
It must be shown that { E , } converges strongly to E. By Lemma 6 , E is in B and so a consideration of the sequence { E. -E } shows that it may be assumed that E 0. Thus , to make an indirect proof , it is assumed that the sequence ...
Page 2462
Moreover , if C belongs to the trace class C1 , then T , C converges to zero in trace norm , and CT * converges to zero in trace norm . PROOF . The set K = C ( { xe H || 2 < 1 } ) is conditionally compact , and thus for each ε > 0 there ...
Moreover , if C belongs to the trace class C1 , then T , C converges to zero in trace norm , and CT * converges to zero in trace norm . PROOF . The set K = C ( { xe H || 2 < 1 } ) is conditionally compact , and thus for each ε > 0 there ...
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
31 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 contained continuous converges Corollary corresponding defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension finite follows formal formula function given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear 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 |