Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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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 H 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 H 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 |
An Operational Calculus for Bounded Spectral | 1941 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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A₁ Acad adjoint operator algebra of projections Amer analytic arbitrary B-algebra B-space B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition dense differential operator Dokl Doklady Akad eigenvalues elements equation exists formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis ibid identity inequality inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR norm normal operators operators in Hilbert perturbation polynomial Proc PROOF properties prove Pure Appl quasi-nilpotent resolution Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose topology trace class type spectral operator unbounded uniformly bounded vector zero