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 2068
... contains all inverses . There are a number of immediate corollaries to this theorem of Wiener which will become apparent from the following lemma . 6 LEMMA . Let 3 be an ideal in the subalgebra A。 of A and let A ( J ) be the algebra of ...
... contains all inverses . There are a number of immediate corollaries to this theorem of Wiener which will become apparent from the following lemma . 6 LEMMA . Let 3 be an ideal in the subalgebra A。 of A and let A ( J ) be the algebra of ...
Page 2159
... contains a non - trivial sub- interval of y . Q.E.D. 12 LEMMA ( G ) . If the point spectrum of the adjoint T * contains no non - trivial subarc of гo , then the set of points regular relative to T is dense in To . PROOF . If is not in ...
... contains a non - trivial sub- interval of y . Q.E.D. 12 LEMMA ( G ) . If the point spectrum of the adjoint T * contains no non - trivial subarc of гo , then the set of points regular relative to T is dense in To . PROOF . If is not in ...
Page 2286
... contains no projection of infinite uniform multiplicity . If A is the closed densely defined linear map of x into ... contains elements of D ( A - 1 ) not belonging to A ( M D ( A ) ) , in which case ( P ( M ) ) contains M properly . Our ...
... contains no projection of infinite uniform multiplicity . If A is the closed densely defined linear map of x into ... contains elements of D ( A - 1 ) not belonging to A ( M D ( A ) ) , in which case ( P ( M ) ) contains M properly . Our ...
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