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 1930
If Eis a Boolean algebra of subsets of the complex plane which contains the void
set and the whole plane , in short , if & is a field of sets in the complex plane , then
a spectral measure E on & is called a resolution of the identity ( or a spectral ...
If Eis a Boolean algebra of subsets of the complex plane which contains the void
set and the whole plane , in short , if & is a field of sets in the complex plane , then
a spectral measure E on & is called a resolution of the identity ( or a spectral ...
Page 2094
12 ) that if X is a weakly complete B - space , then any prespectral operator is
automatically spectral , and so has a unique resolution of the identity . Berkson
and Dowson [ 1 ] have considered prespectral operators in some detail and have
...
12 ) that if X is a weakly complete B - space , then any prespectral operator is
automatically spectral , and so has a unique resolution of the identity . Berkson
and Dowson [ 1 ] have considered prespectral operators in some detail and have
...
Page 2242
The projection valued measure E is said to be the resolution of the identity for T .
13 LEMMA . An unbounded spectral operator of scalar type in the sense of
Definition 12 is a spectral operator in the sense of Definition 1 . Moreover , the ...
The projection valued measure E is said to be the resolution of the identity for T .
13 LEMMA . An unbounded spectral operator of scalar type in the sense of
Definition 12 is a spectral operator in the sense of Definition 1 . Moreover , the ...
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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 |