Linear Operators: Spectral operators |
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Page 2084
... B ) is analytic for > 0 , prove that C is a quasi - nilpotent operator and that R ( λ ; A ) = R ( λ ; B ) + R ( λ ; C ) — I λ 55 ( McCarthy ) Let T be a spectral operator in a complex B - space X which satisfies the growth condition ...
... B ) is analytic for > 0 , prove that C is a quasi - nilpotent operator and that R ( λ ; A ) = R ( λ ; B ) + R ( λ ; C ) — I λ 55 ( McCarthy ) Let T be a spectral operator in a complex B - space X which satisfies the growth condition ...
Page 2193
... B - space , for it has been shown by Kakutani [ 15 ] that the sum of two commuting scalar type spectral operators in a space of continuous functions need not be a spectral operator . However , if n = 1 in Corollary 15 , then the Hilbert ...
... B - space , for it has been shown by Kakutani [ 15 ] that the sum of two commuting scalar type spectral operators in a space of continuous functions need not be a spectral operator . However , if n = 1 in Corollary 15 , then the Hilbert ...
Page 2484
... B ( c ) Show that + ∞ lim 8 ∞ - + 0 + 3 B ( 8 , σ ) στ ίε do - ∞ + B ( 8 , σ ) do FiπA ( s , 8 ) . σ Let be a Hilbert space , and let B ( S ) be the B - space of all bounded operators in H. Let C ( s , t ) be a B ( S ) -valued ...
... B ( c ) Show that + ∞ lim 8 ∞ - + 0 + 3 B ( 8 , σ ) στ ίε do - ∞ + B ( 8 , σ ) do FiπA ( s , 8 ) . σ Let be a Hilbert space , and let B ( S ) be the B - space of all bounded operators in H. Let C ( s , t ) be a B ( S ) -valued ...
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