Linear Operators: Spectral operators |
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Page 2094
... subspace Y≤ X and one of its complements ( that is , if T commutes with some projection of X onto Y ) , then the restriction T | Y of T to Y is spectral . The situation corresponding to an invariant closed subspace of T is not so ...
... subspace Y≤ X and one of its complements ( that is , if T commutes with some projection of X onto Y ) , then the restriction T | Y of T to Y is spectral . The situation corresponding to an invariant closed subspace of T is not so ...
Page 2113
... subspace may have spectrum larger than o ( T ) . Foias [ 12 ] defined a closed linear subspace of a B - space X to be a spectral maximal subspace of T = B ( X ) if ( i ) Y is invariant under T , and ( ii ) if 3 is a closed linear subspace ...
... subspace may have spectrum larger than o ( T ) . Foias [ 12 ] defined a closed linear subspace of a B - space X to be a spectral maximal subspace of T = B ( X ) if ( i ) Y is invariant under T , and ( ii ) if 3 is a closed linear subspace ...
Page 2114
... subspace E ( F ) X is a spectral maximal subspace for T. Similarly if o is a spectral set ( in the sense of VII.3.17 ) and if E , is the corresponding projection operator , then EX is a spectral maximal subspace of T. Hence both ...
... subspace E ( F ) X is a spectral maximal subspace for T. Similarly if o is a spectral set ( in the sense of VII.3.17 ) and if E , is the corresponding projection operator , then EX is a spectral maximal subspace of T. Hence both ...
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