Linear Operators: Spectral operators |
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Page 1951
... belong to the right ( left ) ideal J in B ( X ) . Then every projection E ( o ) with 0 ₫ ō belongs to J. If I is closed , then S and N also belong to J. PROOF . Let 0 ō and let T. = TE ( o ) E ( o ) X , the restriction of T to the ...
... belong to the right ( left ) ideal J in B ( X ) . Then every projection E ( o ) with 0 ₫ ō belongs to J. If I is closed , then S and N also belong to J. PROOF . Let 0 ō and let T. = TE ( o ) E ( o ) X , the restriction of T to the ...
Page 2263
... belongs to the continuous spectrum of the spectral operator S. The point vo belongs to the point or to the continuous spectrum of the operator S depending on whether vo is or is not an eigenvalue of S. PROOF . It follows from Lemma 19 ...
... belongs to the continuous spectrum of the spectral operator S. The point vo belongs to the point or to the continuous spectrum of the operator S depending on whether vo is or is not an eigenvalue of S. PROOF . It follows from Lemma 19 ...
Page 2264
... belongs to the point ( respectively residual or continuous ) spectrum of S if and only if it belongs to the point ( respectively residual or continuous ) spectrum of S2 . Since S2 is a spectral operator of scalar type , we have ( S2 — v ...
... belongs to the point ( respectively residual or continuous ) spectrum of S if and only if it belongs to the point ( respectively residual or continuous ) spectrum of S2 . Since S2 is a spectral operator of scalar type , we have ( S2 — v ...
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