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 1955
... spectrum , and the spectral points of an operator in X will be classified , as they were in Hilbert space , according to the following definition . → 1 DEFINITION . Let ... SPECTRUM OF A SPECTRAL OPERATOR The Spectrum of a Spectral Operator.
... spectrum , and the spectral points of an operator in X will be classified , as they were in Hilbert space , according to the following definition . → 1 DEFINITION . Let ... SPECTRUM OF A SPECTRAL OPERATOR The Spectrum of a Spectral Operator.
Page 1956
... spectrum is void and a point is in its point spectrum if and only if E ( { \ } ) # 0 . PROOF . Let A be a spectral point of T. If E ( { ^ } ) - 0 then E ( { } ) x = x for some x 0 and Nn 0 for some n . It follows from Theorem 2 that À ...
... spectrum is void and a point is in its point spectrum if and only if E ( { \ } ) # 0 . PROOF . Let A be a spectral point of T. If E ( { ^ } ) - 0 then E ( { } ) x = x for some x 0 and Nn 0 for some n . It follows from Theorem 2 that À ...
Page 1957
... spectrum of S. since , according to Theorem 3 , S. , being of finite type , has no residual spectrum . x = σ Q.E.D. - In Theorem 3 the requirement that the spectral operator be of finite type is quite essential . The following ...
... spectrum of S. since , according to Theorem 3 , S. , being of finite type , has no residual spectrum . x = σ Q.E.D. - In Theorem 3 the requirement that the spectral operator be of finite type is quite essential . The following ...
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