Linear Operators: Spectral operators |
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Page 2150
... contained in a spectral set of arbitrarily small diameter and thus in an S ( T ) set of arbitrarily small diameter . Since it is clear that every subset of the resolvent set is an ( T ) set , condition ( D ) is im- mediate . let To ...
... contained in a spectral set of arbitrarily small diameter and thus in an S ( T ) set of arbitrarily small diameter . Since it is clear that every subset of the resolvent set is an ( T ) set , condition ( D ) is im- mediate . let To ...
Page 2234
... contained in U , it may be supposed , since ƒ ( T ) is independent of { e } , that e = e1 . If x is in E ( e ) X , then , by the paragraph preceding Definition 8 , f ( T | E ( en ) X ) x = ƒ ( T | E ( e ) X ) x for n ≥1 so that ƒ ( T ) ...
... contained in U , it may be supposed , since ƒ ( T ) is independent of { e } , that e = e1 . If x is in E ( e ) X , then , by the paragraph preceding Definition 8 , f ( T | E ( en ) X ) x = ƒ ( T | E ( e ) X ) x for n ≥1 so that ƒ ( T ) ...
Page 2256
... contained in an arbitrarily small compact subset σ of o ( T ) which is open in the relative . topology of o ( T ) . It follows that the set 7 ( σ ) = { z | z ̄1 e σ } is a compact subset of o ( R ) , open in the relative topology of o ...
... contained in an arbitrarily small compact subset σ of o ( T ) which is open in the relative . topology of o ( T ) . It follows that the set 7 ( σ ) = { z | z ̄1 e σ } is a compact subset of o ( R ) , open in the relative topology of o ...
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