Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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Page 2219
... finite number of Jordan arcs , no two of which intersect in more than a finite number of points , then V has the required property . α PROOF . Since the operators T are scalar type XVII.4.1 2219 STRONG LIMITS OF SPECTRAL OPERATORS.
... finite number of Jordan arcs , no two of which intersect in more than a finite number of points , then V has the required property . α PROOF . Since the operators T are scalar type XVII.4.1 2219 STRONG LIMITS OF SPECTRAL OPERATORS.
Page 2338
... finite number of the roots of M ( μ ) = 0 which lie in A1 are simple , and that they may be enumerated in a sequence έm in such a way that we have an asymptotic expression 1 ( 49 ) m ~ 2m ( 1 ~ 2 ′′ m ( 1 + £ Сп т m- " ) . n = 1 The ...
... finite number of the roots of M ( μ ) = 0 which lie in A1 are simple , and that they may be enumerated in a sequence έm in such a way that we have an asymptotic expression 1 ( 49 ) m ~ 2m ( 1 ~ 2 ′′ m ( 1 + £ Сп т m- " ) . n = 1 The ...
Page 2362
... finite number of the points in o ( 1 ' ) are simple poles of the resolvent function R ( λ ; T ) ; let { U1 } be a sequence of bounded domains covering the entire plane , such that lim¡ → ∞ minze Ut = ∞ . It is assumed that the ...
... finite number of the points in o ( 1 ' ) are simple poles of the resolvent function R ( λ ; T ) ; let { U1 } be a sequence of bounded domains covering the entire plane , such that lim¡ → ∞ minze Ut = ∞ . It is assumed that the ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
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 linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain E₁ 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