Linear Operators: Spectral operators |
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Page 2188
... Borel measurable functions g for which √ 9 ( μ ) E1 ( dμ ) = { _g ( f ( x ) ) E ( dA ) f ( 4 ) is clearly linear and closed in the set of all bounded Borel functions . Since this set contains every characteristic function of a Borel ...
... Borel measurable functions g for which √ 9 ( μ ) E1 ( dμ ) = { _g ( f ( x ) ) E ( dA ) f ( 4 ) is clearly linear and closed in the set of all bounded Borel functions . Since this set contains every characteristic function of a Borel ...
Page 2233
... Borel sets whose closures are in U , by the equation e Q。x = ƒ ( T | E ( e ) X ) x , x = E ( e ) X . Now , using the machinery established in Lemma 6 , ƒ ( T ) may be defined as follows . = 8 DEFINITION . Let T be a spectral operator ...
... Borel sets whose closures are in U , by the equation e Q。x = ƒ ( T | E ( e ) X ) x , x = E ( e ) X . Now , using the machinery established in Lemma 6 , ƒ ( T ) may be defined as follows . = 8 DEFINITION . Let T be a spectral operator ...
Page 2262
... Borel function vanishing at λ = 0 and at λ = vō1 . A repetition of this argument shows that ( 5 ) still holds if f and g are both bounded Borel functions vanishing at λ = 0 and at λ = võ1 . Since it is obvious from ( 4 ) that T ( ƒ ) ...
... Borel function vanishing at λ = 0 and at λ = vō1 . A repetition of this argument shows that ( 5 ) still holds if f and g are both bounded Borel functions vanishing at λ = 0 and at λ = võ1 . Since it is obvious from ( 4 ) that T ( ƒ ) ...
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