Linear Operators: Spectral operators |
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Page 2095
... scalar type operators also hold for their quotients . Y Although the restrictions of operators with the single valued extension property have this property ( see Dowson [ 1 ] ) , the corresponding result for quotients is not true ...
... scalar type operators also hold for their quotients . Y Although the restrictions of operators with the single valued extension property have this property ( see Dowson [ 1 ] ) , the corresponding result for quotients is not true ...
Page 2106
... scalar type operator of class ( X ) , and ( ii ) if x is weakly complete , then A2 is a scalar type operator . Moreover , if A is adjoint Abelian and is weakly complete , then A is scalar type if and only if either ( a ) A is invertible ...
... scalar type operator of class ( X ) , and ( ii ) if x is weakly complete , then A2 is a scalar type operator . Moreover , if A is adjoint Abelian and is weakly complete , then A is scalar type if and only if either ( a ) A is invertible ...
Page 2174
... scalar type operator with real spectrum . ( This follows from Lemma XV.6.1 which implies that the bounded group G = { ettT | te R } is equivalent to a group of unitary operators . By Stone's theorem , the latter group has an infinitesi ...
... scalar type operator with real spectrum . ( This follows from Lemma XV.6.1 which implies that the bounded group G = { ettT | te R } is equivalent to a group of unitary operators . By Stone's theorem , the latter group has an infinitesi ...
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