Linear Operators: Spectral operators |
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Page 2154
... interval of constancy relative to T is a non - void open subinterval of à ̧ upon which some index function for T is constant . A point λ in T。 is said to be regular relative to T if it belongs to an interval of constancy and if , in ...
... interval of constancy relative to T is a non - void open subinterval of à ̧ upon which some index function for T is constant . A point λ in T。 is said to be regular relative to T if it belongs to an interval of constancy and if , in ...
Page 2159
... interval of y . Q.E.D. 12 LEMMA ( G ) . If the point spectrum of the adjoint T * contains no non - trivial subarc of To , then the set of points regular relative to T is dense in To PROOF . If is not in the point spectrum of the adjoint ...
... interval of y . Q.E.D. 12 LEMMA ( G ) . If the point spectrum of the adjoint T * contains no non - trivial subarc of To , then the set of points regular relative to T is dense in To PROOF . If is not in the point spectrum of the adjoint ...
Page 2160
... interval of constancy relative to T consists entirely of regular points . 0 PROOF . In view of Lemma 11 it suffices to show that a point λ 。 in an interval of constancy relative to T is regular . Since o ( T * ) = σ ( T ) and R ( λ ; T ...
... interval of constancy relative to T consists entirely of regular points . 0 PROOF . In view of Lemma 11 it suffices to show that a point λ 。 in an interval of constancy relative to T is regular . Since o ( T * ) = σ ( T ) and R ( λ ; T ...
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