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 , Ex 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 , Ex 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 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 type ...
... Limits of Spectral Operators : Non - Commutative Case 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 type ...
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 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
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A₁ algebra Amer analytic applications arbitrary B-space Banach Banach space Boolean algebra Borel sets boundary bounded Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator Doklady Akad elements equation equivalent established example exists extension finite follows formula function given gives H₁ Hence Hilbert space hypothesis identity integral invariant inverse Lemma limit linear operators Math multiplicity Nauk SSSR norm normal perturbation plane positive preceding present problem Proc projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero