Linear Operators: Spectral operators |
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Page 2209
... closed algebra generated by B. Q.E.D. 15 COROLLARY . The weakly closed operator algebra generated by a o - complete Boolean algebra B which satisfies the condition of the preceding lemma is the same as the uniformly closed algebra ...
... closed algebra generated by B. Q.E.D. 15 COROLLARY . The weakly closed operator algebra generated by a o - complete Boolean algebra B which satisfies the condition of the preceding lemma is the same as the uniformly closed algebra ...
Page 2214
... closed operator algebra W ( B ) generated by B is the same as the strongly closed algebra generated by B. Thus every A in W ( B ) is the strong limit of finite linear combinations of elements of B. It follows that A leaves invariant ...
... closed operator algebra W ( B ) generated by B is the same as the strongly closed algebra generated by B. Thus every A in W ( B ) is the strong limit of finite linear combinations of elements of B. It follows that A leaves invariant ...
Page 2217
... closed linear manifolds generated by the sets { ExE ¤ B } , { Ex | E ¤ B1 } , respectively . Since B1 is the strong closure of B , each element Ex with E in ... closed operator algebra generated by B ) XVII.3.24 2217 STRONGLY CLOSED ALGEBRAS.
... closed linear manifolds generated by the sets { ExE ¤ B } , { Ex | E ¤ B1 } , respectively . Since B1 is the strong closure of B , each element Ex with E in ... closed operator algebra generated by B ) XVII.3.24 2217 STRONGLY CLOSED ALGEBRAS.
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