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 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain eigenvalues elements equation exists finite number follows from Lemma follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero