Linear Operators: Spectral operators |
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Page 1938
Nelson Dunford, Jacob T. Schwartz. N and an operator S which is of scalar type in accordance with the follow- ing definition . ➡ 1 DEFINITION . A bounded operator S is said to be of scalar type in case it is a spectral operator which ...
Nelson Dunford, Jacob T. Schwartz. N and an operator S which is of scalar type in accordance with the follow- ing definition . ➡ 1 DEFINITION . A bounded operator S is said to be of scalar type in case it is a spectral operator which ...
Page 2111
... operator in l2 , or a quasi- nilpotent operator with empty point spectrum . It is proved that if m is a T - measure , then m vanishes outside o ( T ) . Moreover , T is a scalar type spectral operator if and only if every vector has a ...
... operator in l2 , or a quasi- nilpotent operator with empty point spectrum . It is proved that if m is a T - measure , then m vanishes outside o ( T ) . Moreover , T is a scalar type spectral operator if and only if every vector has a ...
Page 2242
... spectral operator of scalar type . The projection valued measure E is said to be the resolution of the identity for T. 13 LEMMA . An unbounded spectral operator of scalar type in the sense of Definition 12 is a spectral operator in the ...
... spectral operator of scalar type . The projection valued measure E is said to be the resolution of the identity for T. 13 LEMMA . An unbounded spectral operator of scalar type in the sense of Definition 12 is a spectral operator in the ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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Common terms and phrases
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