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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Results 1-3 of 87
Page 1983
... preceding corollary shows that A is a spectral operator . Since  ( s ) has distinct eigenvalues , it is a scalar operator , that is , its radical part is zero . Thus Corollary 9 shows that A is also a scalar type operator . Q.E.D. 11 ...
... preceding corollary shows that A is a spectral operator . Since  ( s ) has distinct eigenvalues , it is a scalar operator , that is , its radical part is zero . Thus Corollary 9 shows that A is also a scalar type operator . Q.E.D. 11 ...
Page 2082
... preceding exercise , let x * , xo , and σ 。 be chosen so that x * E ( oo ) xo 0 and let g be the Radon - Nikodım deriva- tive of x * E ( ) x 。 with respect to μ . There is a subset σ1 of σ on which g 01 σ 。 is bounded away from zero ...
... preceding exercise , let x * , xo , and σ 。 be chosen so that x * E ( oo ) xo 0 and let g be the Radon - Nikodım deriva- tive of x * E ( ) x 。 with respect to μ . There is a subset σ1 of σ on which g 01 σ 。 is bounded away from zero ...
Page 2232
... preceding theorem it follows that E ( e ) D ( Q ) ≤ D ( Q ) and QE ( e ) x = E ( e ) Qx for every x in D ( Q ) and every e in Σ . PROOF . Let { e } be as in the preceding proof , and let x be in D ( Q ) . Then lim , E ( e ) E ( e , ) x ...
... preceding theorem it follows that E ( e ) D ( Q ) ≤ D ( Q ) and QE ( e ) x = E ( e ) Qx for every x in D ( Q ) and every e in Σ . PROOF . Let { e } be as in the preceding proof , and let x be in D ( Q ) . Then lim , E ( e ) E ( e , ) x ...
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero