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 ... 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 ... SPECTRUM OF A SPECTRAL OPERATOR The Spectrum of a Spectral Operator.
Page 1956
... spectrum is void and a point A is in its point spectrum if and only if E ( { X } ) # 0 . PROOF . Let be a spectral point of T. If E ( { } ) # 0 then E ( { A } ) x = x for some x 0 and Nn 0 for some n . It follows from Theorem 2 that ...
... spectrum is void and a point A is in its point spectrum if and only if E ( { X } ) # 0 . PROOF . Let be a spectral point of T. If E ( { } ) # 0 then E ( { A } ) x = x for some x 0 and Nn 0 for some n . It follows from Theorem 2 that ...
Page 1957
... spectrum of S. since , according to Theorem 3 , S. , being of finite type , has no residual spectrum . σ Q.E.D. - In Theorem 3 the requirement that the spectral operator be of finite type is quite essential . The following elementary ...
... spectrum of S. since , according to Theorem 3 , S. , being of finite type , has no residual spectrum . σ Q.E.D. - In Theorem 3 the requirement that the spectral operator be of finite type is quite essential . The following elementary ...
Contents
SPECTRAL OPERATORS | 1924 |
The Spectrum of a Spectral Operator | 1955 |
The Algebras A and | 1966 |
Copyright | |
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A₁ Acad adjoint operator algebra of projections Amer analytic arbitrary B-algebra B-space 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 dense differential operator Dokl Doklady Akad eigenvalues elements equation exists formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis ibid identity inequality invariant subspaces inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR nonselfadjoint norm normal operators operators in Hilbert perturbation Proc PROOF properties prove Pures Appl quasi-nilpotent resolution Russian satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose topology trace class type spectral operator unbounded uniformly bounded vector zero