Linear Operators: Spectral operators |
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Results 1-3 of 94
Page 1951
... bounded linear operator in the space E ( X ) . Let V , be the bounded linear operator in X defined by the equation σ 1 V ̧x = T - 1E ( o ) x , x = x . σ - σ Then TV = E ( o ) = V , T , which proves that E ( o ) is in J. It follows from ...
... bounded linear operator in the space E ( X ) . Let V , be the bounded linear operator in X defined by the equation σ 1 V ̧x = T - 1E ( o ) x , x = x . σ - σ Then TV = E ( o ) = V , T , which proves that E ( o ) is in J. It follows from ...
Page 2143
... bounded linear operator in the complex B - space X. Then there is a unique spectral measure on the field S ( T ) with the properties E ( S ) x = x , SES ( T ) , σ ( x ) = 8 , = = 0 , d = S ( T ) , σ ( x ) ≤ d ' . This spectral measure ...
... bounded linear operator in the complex B - space X. Then there is a unique spectral measure on the field S ( T ) with the properties E ( S ) x = x , SES ( T ) , σ ( x ) = 8 , = = 0 , d = S ( T ) , σ ( x ) ≤ d ' . This spectral measure ...
Page 2162
... bounded linear operator in the B - space X which satisfies conditions ( B ) and ( G ) and let B be the field of Borel sets in the plane . Then the adjoint T * is a spectral operator of class ( B , X ) provided that any one of the ...
... bounded linear operator in the B - space X which satisfies conditions ( B ) and ( G ) and let B be the field of Borel sets in the plane . Then the adjoint T * is a spectral operator of class ( B , X ) provided that any one of the ...
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