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
The operators we shall study in the next few chapters will be operators which
have a resolution of the identity with ... We shall , in fact , study resolutions of the
identity which are countably additive on the field B of Borel sets in the plane .
The operators we shall study in the next few chapters will be operators which
have a resolution of the identity with ... We shall , in fact , study resolutions of the
identity which are countably additive on the field B of Borel sets in the plane .
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 | 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 |