Linear Operators: Spectral operators |
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Page 2256
... Suppose that o ( T ) is totally disconnected . Then T is a spectral operator if and only if ( a ) the family of projections E ( o ; T ) corresponding to compact spectral sets of T is uniformly bounded , and ( b ) no non - zero x in X ...
... Suppose that o ( T ) is totally disconnected . Then T is a spectral operator if and only if ( a ) the family of projections E ( o ; T ) corresponding to compact spectral sets of T is uniformly bounded , and ( b ) no non - zero x in X ...
Page 2284
... suppose the sets en are disjoint and Un = 1 en = P , the whole plane . = n סא ... " * 1 , ... , xn * Now consider n fixed and suppose En 0. It follows from Lemma 18 and Theorem 19 that there exist vectors x1 , x and functions x1 , such ...
... suppose the sets en are disjoint and Un = 1 en = P , the whole plane . = n סא ... " * 1 , ... , xn * Now consider n fixed and suppose En 0. It follows from Lemma 18 and Theorem 19 that there exist vectors x1 , x and functions x1 , such ...
Page 2303
... Suppose that E is its resolution of the identity , and suppose that { n } is an enumeration of its spectrum . Let d , denote the distance from λ , to o ( T ) — { \ n } . Suppose that for all but a finite number of n , E ( ^ „ ) has a ...
... Suppose that E is its resolution of the identity , and suppose that { n } is an enumeration of its spectrum . Let d , denote the distance from λ , to o ( T ) — { \ n } . Suppose that for all but a finite number of n , E ( ^ „ ) has a ...
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