Linear Operators: Spectral operators |
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Page 2154
Nelson Dunford, Jacob T. Schwartz. ( G ) The spectrum of T is contained in the rectifiable Jordan curve To . Moreover , there is an integer valued function v defined on T。 such that for every λo in To , | ( λ — λ 。) » ‹ 1o ) R ( λ ; T ) ...
Nelson Dunford, Jacob T. Schwartz. ( G ) The spectrum of T is contained in the rectifiable Jordan curve To . Moreover , there is an integer valued function v defined on T。 such that for every λo in To , | ( λ — λ 。) » ‹ 1o ) R ( λ ; T ) ...
Page 2159
... 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 of T , then there is no functional x * 0 for which x * ( \ I − T ) X = 0 ...
... 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 of T , then there is no functional x * 0 for which x * ( \ I − T ) X = 0 ...
Page 2160
... to T are dense in To and , in particular , every 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 ...
... to T are dense in To and , in particular , every 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 ...
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