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 2242
T = T ( s ) in the sense of Definition 10 , where f ( z ) = 2 , then T is said to be an unbounded spectral operator of scalar type . The projection valued measure E is said to be the resolution of the identity for T. 13 LEMMA .
T = T ( s ) in the sense of Definition 10 , where f ( z ) = 2 , then T is said to be an unbounded spectral operator of scalar type . The projection valued measure E is said to be the resolution of the identity for T. 13 LEMMA .
Page 2590
Restriction of a spectral operator , spectrum of , XV.8.5 ( 1956 ) Quantum mechanical three - body problem , XX.6 ( 2501 ) , ( 2507 ) Quantum theory of fields , XX.6 ( 2501 ) , ( 2507 ) Quasi - nilpotent operator , definition of ...
Restriction of a spectral operator , spectrum of , XV.8.5 ( 1956 ) Quantum mechanical three - body problem , XX.6 ( 2501 ) , ( 2507 ) Quantum theory of fields , XX.6 ( 2501 ) , ( 2507 ) Quasi - nilpotent operator , definition of ...
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countably additive , XV.2 ( 1930 ) , XV.2.3 ( 1930 ) , XV.2.4 ( 1931 ) definition of , XV.2.1 ( 1929 ) integral with respect to , XV.2 ( 1929 ) Spectral operator , adjoint of , XVI.4.6 ( 2148 ) , XVI.5.16 ( 2162 ) canonical reduction of ...
countably additive , XV.2 ( 1930 ) , XV.2.3 ( 1930 ) , XV.2.4 ( 1931 ) definition of , XV.2.1 ( 1929 ) integral with respect to , XV.2 ( 1929 ) Spectral operator , adjoint of , XVI.4.6 ( 2148 ) , XVI.5.16 ( 2162 ) canonical reduction of ...
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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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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 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 |