Linear Operators: Spectral operators |
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Page 2084
... B ) is analytic for λ # 0 , prove that C is a quasi - nilpotent operator and that R ( \ ; A ) = R ( \ ; B ) + R ( \ ; C ) - I 55 ( McCarthy ) Let T be a spectral operator in a complex B - space X which satisfies the growth condition ...
... B ) is analytic for λ # 0 , prove that C is a quasi - nilpotent operator and that R ( \ ; A ) = R ( \ ; B ) + R ( \ ; C ) - I 55 ( McCarthy ) Let T be a spectral operator in a complex B - space X which satisfies the growth condition ...
Page 2193
... B - space , for it has been shown by Kakutani [ 15 ] that the sum of two commuting scalar type spectral operators in a space of continuous functions need not be a spectral operator . However , if n = 1 in Corollary 15 , then the Hilbert ...
... B - space , for it has been shown by Kakutani [ 15 ] that the sum of two commuting scalar type spectral operators in a space of continuous functions need not be a spectral operator . However , if n = 1 in Corollary 15 , then the Hilbert ...
Page 2482
... B - space of sequences z = [ 20 , 21 , ... ] with the norm | z | = { Σ = 0 | , \ " } 1 / P , and let A be the B - space of infinite matrices a = { a1 , i , j ≥ 0 } such that || a || = Σ | α , < ∞ . at i , j = 0 Let B be the B - space ...
... B - space of sequences z = [ 20 , 21 , ... ] with the norm | z | = { Σ = 0 | , \ " } 1 / P , and let A be the B - space of infinite matrices a = { a1 , i , j ≥ 0 } such that || a || = Σ | α , < ∞ . at i , j = 0 Let B be the B - space ...
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