Linear Operators: Spectral operators |
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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 I 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 I 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 T 。. 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 T 。. 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 ( MD ( 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 ( MD ( A ) ) , in which case ( P ( M ) ) contains M properly . Our ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero