Linear Operators: Spectral operators |
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Page 2222
... constant A such that | f ( T ) | = A \ f \ , fe R ( o ( T ) ) . 3 Let be a reflexive B - space and Te B ( X ) and suppose that σ ( T ) is an R - set . Then T is a scalar type spectral operator if and only if there exists a constant A ...
... constant A such that | f ( T ) | = A \ f \ , fe R ( o ( T ) ) . 3 Let be a reflexive B - space and Te B ( X ) and suppose that σ ( T ) is an R - set . Then T is a scalar type spectral operator if and only if there exists a constant A ...
Page 2439
... constant co such co sin ( 0/2 ) | for 0≤ | 0 | ≤ 7/2 , formula ( 30 ) follows at once . Using ( 27 ) , ( 30 ) , and ( 31 ) , we see that there exists a finite constant M ' independent of ε such that ( 33 ) | √ ( rw — r'w ' ) | ≤ M'ɛ ...
... constant co such co sin ( 0/2 ) | for 0≤ | 0 | ≤ 7/2 , formula ( 30 ) follows at once . Using ( 27 ) , ( 30 ) , and ( 31 ) , we see that there exists a finite constant M ' independent of ε such that ( 33 ) | √ ( rw — r'w ' ) | ≤ M'ɛ ...
Page 2441
... constant c ' such that I ( a ) | ≤ c ' ( 1+ | x | ) -n + 1 . Using this inequality and using ( 37 ) , we see that there exists a finite constant M " independent of ɛ such that av 4 Ər 4 r ' ) V 4 ( r , r ' ) ( 43 ) | Var , r ' ) | + ...
... constant c ' such that I ( a ) | ≤ c ' ( 1+ | x | ) -n + 1 . Using this inequality and using ( 37 ) , we see that there exists a finite constant M " independent of ɛ such that av 4 Ər 4 r ' ) V 4 ( r , r ' ) ( 43 ) | Var , r ' ) | + ...
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