Linear Operators: Spectral operators |
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Page 1948
... commutes with A * . PROOF . This is a corollary of Corollary 3.7 . Q.E.D. 2 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 . Q.E.D. 2 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 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero