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 2094
It follows from some results of Bade [ 4 ] ( see also XVII.2.1 and XVII.2.12 ) 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 .
It follows from some results of Bade [ 4 ] ( see also XVII.2.1 and XVII.2.12 ) 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 .
Page 2143
Let T be a bounded linear operator in the complex B - space X. Then there is a unique spectral measure on the field S ( T ) with the properties = E ( 8 ) x = x , = 0 , SES ( T ) , ( x ) So , de S ( T ) , g ( x ) = 8 ' .
Let T be a bounded linear operator in the complex B - space X. Then there is a unique spectral measure on the field S ( T ) with the properties = E ( 8 ) x = x , = 0 , SES ( T ) , ( x ) So , de S ( T ) , g ( x ) = 8 ' .
Page 2184
It will be seen in the following theorem that an arbitrary isomorphic homeomorphism of the algebra A ( B ) onto the algebra of continuous functions on its structure space may be represented by an integral with respect to a uniquely ...
It will be seen in the following theorem that an arbitrary isomorphic homeomorphism of the algebra A ( B ) onto the algebra of continuous functions on its structure space may be represented by an integral with respect to a uniquely ...
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
47 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 contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension 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 |