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 2263
... belongs to the continuous spectrum of the spectral operator S. The point v 。 belongs to the point or to the continuous spectrum of the operator S depending on whether vo is or is not an eigenvalue of S. - PROOF . It follows from Lemma ...
... belongs to the continuous spectrum of the spectral operator S. The point v 。 belongs to the point or to the continuous spectrum of the operator S depending on whether vo is or is not an eigenvalue of S. - PROOF . It follows from Lemma ...
Page 2264
... belongs to the point ( respectively residual or continuous ) spectrum of S if and only if it belongs to the point ( respectively residual or continuous ) spectrum of S2 . Since S2 is a spectral operator of scalar type , we have ( S2 — v ...
... belongs to the point ( respectively residual or continuous ) spectrum of S if and only if it belongs to the point ( respectively residual or continuous ) spectrum of S2 . Since S2 is a spectral operator of scalar type , we have ( S2 — v ...
Page 2462
... belongs to the trace class . Then , by what we have already proved , T , A converges to zero in norm , and thus , by Lemma XI.9.9 , TC = ( TA ) B converges to zero in trace norm . By Lemma XI.9.6 ( c ) and Definition XI.9.1 , C * belongs ...
... belongs to the trace class . Then , by what we have already proved , T , A converges to zero in norm , and thus , by Lemma XI.9.9 , TC = ( TA ) B converges to zero in trace norm . By Lemma XI.9.6 ( c ) and Definition XI.9.1 , C * belongs ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
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