Linear Operators: Spectral operators |
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Page 2125
... Borel subsets of C which is maximal ( in a certain sense ) and that such an extension is uniquely determined . In fact , let Do ( P ) consist of the set of all Borel sets d≤ С such that sup { | P ( 0 ) || σ € D ( P ) , o ≤ 8 } < + ...
... Borel subsets of C which is maximal ( in a certain sense ) and that such an extension is uniquely determined . In fact , let Do ( P ) consist of the set of all Borel sets d≤ С such that sup { | P ( 0 ) || σ € D ( P ) , o ≤ 8 } < + ...
Page 2202
... set A of maximal ideals , and any homeomorphic isomorphism T between these algebras uniquely determines a regular countably additive spectral measure E in X defined on the family of Borel sets in A and such that T ( ƒ ) = ƒ ƒ ( \ ) E ...
... set A of maximal ideals , and any homeomorphic isomorphism T between these algebras uniquely determines a regular countably additive spectral measure E in X defined on the family of Borel sets in A and such that T ( ƒ ) = ƒ ƒ ( \ ) E ...
Page 2233
... set U such that E ( U ) I. Let { e } be an arbitrary increasing sequence of bounded Borel sets with closures contained in U , such that E ( U - 1 en ) = I. The operator f ( T ) is defined by the equations n D ( ƒ ( T ' ) ) = { x | lim ƒ ...
... set U such that E ( U ) I. Let { e } be an arbitrary increasing sequence of bounded Borel sets with closures contained in U , such that E ( U - 1 en ) = I. The operator f ( T ) is defined by the equations n D ( ƒ ( T ' ) ) = { x | lim ƒ ...
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