Linear Operators: Spectral operators |
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Page 2169
... continuous functions . To see that it is a homomorphism on the algebra of bounded Borel functions , note that for a fixed continuous function g the set of all bounded Borel functions ƒ for which ( vi ) ( fg ) ( T ) = ƒ ( T ) g ( T ) ...
... continuous functions . To see that it is a homomorphism on the algebra of bounded Borel functions , note that for a fixed continuous function g the set of all bounded Borel functions ƒ for which ( vi ) ( fg ) ( T ) = ƒ ( T ) g ( T ) ...
Page 2199
... continuous functions on the space of maximal ideals in A ( B ) . Moreover , by Theorem 2.5 , this iso- morphism S ... function f1 , and since E2E , we have ƒ2 = fn , which shows that f , assumes only the values zero and one and is therefore ...
... continuous functions on the space of maximal ideals in A ( B ) . Moreover , by Theorem 2.5 , this iso- morphism S ... function f1 , and since E2E , we have ƒ2 = fn , which shows that f , assumes only the values zero and one and is therefore ...
Page 2261
... function f on o ( T ) , a continuous bilinear form ( f , yo , yo ) , which , since Do and * are dense , has a unique extension to a bounded bilinear ... continuous functions vanishing at λ = 0 XVIII.2.34 2261 UNBOUNDED SPECTRAL OPERATORS.
... function f on o ( T ) , a continuous bilinear form ( f , yo , yo ) , which , since Do and * are dense , has a unique extension to a bounded bilinear ... continuous functions vanishing at λ = 0 XVIII.2.34 2261 UNBOUNDED SPECTRAL OPERATORS.
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