Linear Operators: Spectral operators |
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Page 1931
... analytic extension of R ( § ; T ) x will be meant an X - valued function f defined and analytic on an open set D ( f ) p ( T ) and such that ( §I — T ) ƒ ( § ) = x , It is clear that , for such an extension , ƒ ( § ) = R ( § ; T ) x ...
... analytic extension of R ( § ; T ) x will be meant an X - valued function f defined and analytic on an open set D ( f ) p ( T ) and such that ( §I — T ) ƒ ( § ) = x , It is clear that , for such an extension , ƒ ( § ) = R ( § ; T ) x ...
Page 1932
... analytic function with domain p ( x ) and with x ( § ) = R ( § ; T ) x , ξερ ( Τ ) . It will be shown in the next section that , if T is a spectral operator , the function R ( § ; T ) x has , for every x in X , the single valued ...
... analytic function with domain p ( x ) and with x ( § ) = R ( § ; T ) x , ξερ ( Τ ) . It will be shown in the next section that , if T is a spectral operator , the function R ( § ; T ) x has , for every x in X , the single valued ...
Page 2248
... analytic in a domain U which , when taken together with a finite number of exceptional points p , includes a ... analytic at infinity , then e1 = f - 1 ( e ) is bounded , and it follows from Theorem 9 ( ii ) that D ( f ( T ) ) ≥ E ( e1 ) ...
... analytic in a domain U which , when taken together with a finite number of exceptional points p , includes a ... analytic at infinity , then e1 = f - 1 ( e ) is bounded , and it follows from Theorem 9 ( ii ) that D ( f ( T ) ) ≥ E ( e1 ) ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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Common terms and phrases
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