Linear Operators: Spectral operators |
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Page 2100
... proved that scalar type operators in a L - space are of a surprisingly special form in that their spectral measures are finite . Thus if S is a scalar type operator in such a space , then S - 1 E. Moreover , every scalar type operator ...
... proved that scalar type operators in a L - space are of a surprisingly special form in that their spectral measures are finite . Thus if S is a scalar type operator in such a space , then S - 1 E. Moreover , every scalar type operator ...
Page 2133
... proved by Dieudonné [ 22 ] for Fredholm operators , although he did not specifically define the index . In 1951 Atkinson proved both stability theorems . In that same year both Yood [ 2 ] and Gohberg [ 7 ] also proved the second theorem ...
... proved by Dieudonné [ 22 ] for Fredholm operators , although he did not specifically define the index . In 1951 Atkinson proved both stability theorems . In that same year both Yood [ 2 ] and Gohberg [ 7 ] also proved the second theorem ...
Page 2225
... proved that a bounded monotone generalized sequence of projections in a reflexive space is strongly convergent to a projection . In the case of Hilbert spaces , Lemma 3.14 was proved by Wolf [ 2 ] . It was observed by F. Riesz [ 21 ] ...
... proved that a bounded monotone generalized sequence of projections in a reflexive space is strongly convergent to a projection . In the case of Hilbert spaces , Lemma 3.14 was proved by Wolf [ 2 ] . It was observed by F. Riesz [ 21 ] ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero