Linear Operators: Spectral operators |
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Page 2194
... closure in the weak as in the strong operator topology . Thus the strong and weak operator closures of an algebra of ... closure of the algebra generated by the projections in its resolution of the identity , the problem of the present ...
... closure in the weak as in the strong operator topology . Thus the strong and weak operator closures of an algebra of ... closure of the algebra generated by the projections in its resolution of the identity , the problem of the present ...
Page 2217
... closure . By Lemma 3 , B is bounded and thus B1 is also a bounded Boolean algebra of projections in X. Suppose that B1 is not complete . By Lemma 4 there is a monotone increasing generalized sequence { E } in B , and an x in X such that ...
... closure . By Lemma 3 , B is bounded and thus B1 is also a bounded Boolean algebra of projections in X. Suppose that B1 is not complete . By Lemma 4 there is a monotone increasing generalized sequence { E } in B , and an x in X such that ...
Page 2234
... closure 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 ...
... closure 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 ...
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