Linear Operators: Spectral operators |
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Page 1931
... clear to begin with that a countably additive resolution of the identity defined on the Borel sets of the plane is uniquely determined by the spectral operator T. This is the case , but until it is proved we refer to any such spectral ...
... clear to begin with that a countably additive resolution of the identity defined on the Borel sets of the plane is uniquely determined by the spectral operator T. This is the case , but until it is proved we refer to any such spectral ...
Page 2053
... clear from the form of exp t that T ( t ) p was differentiable for t > 0 and an arbitrary in H " . It is even clear that the nth order derivative T ) ( t ) exists in the uniform operator topology for t > 0 and every positive integer n ...
... clear from the form of exp t that T ( t ) p was differentiable for t > 0 and an arbitrary in H " . It is even clear that the nth order derivative T ) ( t ) exists in the uniform operator topology for t > 0 and every positive integer n ...
Page 2159
... clear that the union of intervals of constancy is open . To see that it is dense , let y be a closed subarc of П having positive length and let Yn = { λo | λo € y , | λ — λ 。| " | R ( λ ; T ) | ≤ 1 , λo ‡ λ € 4 xo } = { λo | λ 。€ y ...
... clear that the union of intervals of constancy is open . To see that it is dense , let y be a closed subarc of П having positive length and let Yn = { λo | λo € y , | λ — λ 。| " | R ( λ ; T ) | ≤ 1 , λo ‡ λ € 4 xo } = { λo | λ 。€ y ...
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