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 1947
Let B1 , ... , Bk be a finite collection of commuting bounded Boolean algebras of projections in a Hilbert space H. Then there exists a bounded self adjoint operator B in H with a bounded everywhere defined inverse such that BEB - 1 is ...
Let B1 , ... , Bk be a finite collection of commuting bounded Boolean algebras of projections in a Hilbert space H. Then there exists a bounded self adjoint operator B in H with a bounded everywhere defined inverse such that BEB - 1 is ...
Page 2170
These lemmas will show that the hypotheses of Theorem 5.18 are satisfied by a self adjoint operator in Hilbert space . 1 LEMMA . If T is a bounded self adjoint operator in Hilbert space , its spectrum is real and for every non - real a ...
These lemmas will show that the hypotheses of Theorem 5.18 are satisfied by a self adjoint operator in Hilbert space . 1 LEMMA . If T is a bounded self adjoint operator in Hilbert space , its spectrum is real and for every non - real a ...
Page 2478
Let H4 be a self adjoint operator in H , with domain D ( H , ) and resolution of the identity E4 ( . ) . Suppose that V4 is a symmetric operator in H , that D ( V4 ) 2D ( H4 ) , that the operator V ( il - H2 ) -1 is compact , and that ...
Let H4 be a self adjoint operator in H , with domain D ( H , ) and resolution of the identity E4 ( . ) . Suppose that V4 is a symmetric operator in H , that D ( V4 ) 2D ( H4 ) , that the operator V ( il - H2 ) -1 is compact , and that ...
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
31 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 contained continuous converges Corollary corresponding defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension finite follows formal formula function given Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear 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 |