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 2323
The labor of verifying Hypothesis 1 may be simplified by using the following
elementary observations . By equations ( 1 ) , ( 4 ) , and our preliminary
normalization of boundary conditions , the terms of order p in the determinant N (
u ) are ...
The labor of verifying Hypothesis 1 may be simplified by using the following
elementary observations . By equations ( 1 ) , ( 4 ) , and our preliminary
normalization of boundary conditions , the terms of order p in the determinant N (
u ) are ...
Page 2397
PROOF . The theorem will follow as soon as it is shown that the hypotheses of
Theorem XVIII . ... Hypothesis ( ii ) has been established and is given by Lemma
7 ( iv ) . It therefore only remains to establish hypothesis ( iii ) of Theorem XVIII . 2
.
PROOF . The theorem will follow as soon as it is shown that the hypotheses of
Theorem XVIII . ... Hypothesis ( ii ) has been established and is given by Lemma
7 ( iv ) . It therefore only remains to establish hypothesis ( iii ) of Theorem XVIII . 2
.
Page 2401
... or , using hypothesis ( b ) , to ( 4 ) P ( B ) – 1 ( B ) ' ( A1 ) = P ( A1 ) . Using
hypothesis ( c ) , we may write this last equation as q ( B – 4 ( B , A1 ) ) = Q ( A1 ) .
Now , by hypothesis , the map B + 4 ( B , A1 ) of A → A has norm at most M2 ( M1
...
... or , using hypothesis ( b ) , to ( 4 ) P ( B ) – 1 ( B ) ' ( A1 ) = P ( A1 ) . Using
hypothesis ( c ) , we may write this last equation as q ( B – 4 ( B , A1 ) ) = Q ( A1 ) .
Now , by hypothesis , the map B + 4 ( B , A1 ) of A → A has norm at most M2 ( M1
...
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Contents
SPECTRAL OPERATORS XV Spectral Operators | 1924 |
Introduction | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
32 other sections not shown
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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 |