Linear Operators: Spectral operators |
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Page 1948
... commutes with A * . PROOF . This is a corollary of Corollary 3.7 . 2 Q.E.D. PROOF OF COROLLARY 5. Let T1 , T2 be commuting spectral operators in Hilbert space 5 and let S1 + N1 , S2 + N2 be their canonical decomposi- tions . It follows ...
... commutes with A * . PROOF . This is a corollary of Corollary 3.7 . 2 Q.E.D. PROOF OF COROLLARY 5. Let T1 , T2 be commuting spectral operators in Hilbert space 5 and let S1 + N1 , S2 + N2 be their canonical decomposi- tions . It follows ...
Page 2098
... commuting quasi - nilpotent . Spectral operators in Hilbert space . The fact that a finite number of commuting spectral operators in a Hilbert space can be simultaneously transformed into normal operators by passing to an equivalent ...
... commuting quasi - nilpotent . Spectral operators in Hilbert space . The fact that a finite number of commuting spectral operators in a Hilbert space can be simultaneously transformed into normal operators by passing to an equivalent ...
Page 2177
... commuting spectral operators in Hilbert space . The attentive reader may have noticed , however , that no attempt ... commuting spectral operators be spectral . At the same time , various sufficient conditions that the uniform , weak ...
... commuting spectral operators in Hilbert space . The attentive reader may have noticed , however , that no attempt ... commuting spectral operators be spectral . At the same time , various sufficient conditions that the uniform , weak ...
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