Linear Operators: Spectral operators |
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Page 2217
... limit lim , Ex does not exist . Let X ( x ) , X1 ( x ) be the closed linear manifolds generated by the sets { ExE ... limit lim , Eax does not exist , the limit lim , E fails to exist in the strong topology . It follows from Lemma 4 that ...
... limit lim , Ex does not exist . Let X ( x ) , X1 ( x ) be the closed linear manifolds generated by the sets { ExE ... limit lim , Eax does not exist , the limit lim , E fails to exist in the strong topology . It follows from Lemma 4 that ...
Page 2219
... Limits of Spectral Operators : Non - Commutative Case Q.E.D. In this section conditions will be given to insure that the strong limit T = lim 。 T。 of a generalized sequence { T } of scalar type spectral opera- tors is itself a scalar ...
... Limits of Spectral Operators : Non - Commutative Case Q.E.D. In this section conditions will be given to insure that the strong limit T = lim 。 T。 of a generalized sequence { T } of scalar type spectral opera- tors is itself a scalar ...
Page 2393
... limit points on the real axis . Consequently , Z is a finite set . Now let λ 。€ Z and let v 。 be the order of λ as ... limit B ( A ) as 80. It is therefore evident that the limit B * ( f , g , λ ) in statement ( iv ) of the present ...
... limit points on the real axis . Consequently , Z is a finite set . Now let λ 。€ Z and let v 。 be the order of λ as ... limit B ( A ) as 80. It is therefore evident that the limit B * ( f , g , λ ) in statement ( iv ) of the present ...
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