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 78
Page 1953
... range of T is closed , it follows from Corollary 12 that TX = X. By Lemma 3.1 the operator T is one - to - one . By ... range of V is closed . Let y be in the closure of the range of V. Then for some sequence { x } in E ( { 0 } ' ) X_we ...
... range of T is closed , it follows from Corollary 12 that TX = X. By Lemma 3.1 the operator T is one - to - one . By ... range of V is closed . Let y be in the closure of the range of V. Then for some sequence { x } in E ( { 0 } ' ) X_we ...
Page 1954
... range if and only if ( i ) the point λ = 0 is either in the resolvent set of T or an isolated spectral point of T , and ( ii ) the operator TE ( { 0 } ) has a closed range . PROOF . Let T have a closed range . We have already proved ( i ) ...
... range if and only if ( i ) the point λ = 0 is either in the resolvent set of T or an isolated spectral point of T , and ( ii ) the operator TE ( { 0 } ) has a closed range . PROOF . Let T have a closed range . We have already proved ( i ) ...
Page 2312
... range of T. On the other hand , if y is not in the closure of the range of T , then by the Hahn - Banach theorem ( II.3.13 ) there exists a y * in * such that y * ( y ) 0 , y * Tz = 0 for z in D ( T ) . Then it follows from Definition 6 ...
... range of T. On the other hand , if y is not in the closure of the range of T , then by the Hahn - Banach theorem ( II.3.13 ) there exists a y * in * such that y * ( y ) 0 , y * Tz = 0 for z in D ( T ) . Then it follows from Definition 6 ...
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
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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