Linear Operators, Part 2 |
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Page 1917
... limit U = lim ettT'e - itT . ∞ +7 This purely formal argument inspires us to study the limit appearing above , and indeed it develops that if the difference TT satisfies suitable hypotheses , this limit will exist in the strong ...
... limit U = lim ettT'e - itT . ∞ +7 This purely formal argument inspires us to study the limit appearing above , and indeed it develops that if the difference TT satisfies suitable hypotheses , this limit will exist in the strong ...
Page 2219
... Limits of Spectral Operators : Non - Commutative Case In this section conditions will be given to insure that the strong limit T = lim 。 Tɑ 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 。 Tɑ 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 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
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Common terms and phrases
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 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