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 2248
... neighborhood of o ( T ) and a neighborhood of the point at infinity . Suppose that each exceptional point p satisfies E ( p ) = 0 , and that f has at most a pole at each of the excep- tional points p and at infinity . Then f ( T ) is a ...
... neighborhood of o ( T ) and a neighborhood of the point at infinity . Suppose that each exceptional point p satisfies E ( p ) = 0 , and that f has at most a pole at each of the excep- tional points p and at infinity . Then f ( T ) is a ...
Page 2255
... neighborhood of o and identically zero in a neighborhood of σ ( T ) – -σ . Then f , is analytic in a neighborhood of o ( T ) and in a neighbor- hood of infinity , so that VII.9.3 f . ( T ) is a well - defined bounded operator . We shall ...
... neighborhood of o and identically zero in a neighborhood of σ ( T ) – -σ . Then f , is analytic in a neighborhood of o ( T ) and in a neighbor- hood of infinity , so that VII.9.3 f . ( T ) is a well - defined bounded operator . We shall ...
Page 2256
... neighborhood of infinity , C1 being oriented in the customary positive sense of complex variable theory . The curves C of the present lemma bound a finite domain D containing every point of σ and no point of o ( T ) - o . It is clear ...
... neighborhood of infinity , C1 being oriented in the customary positive sense of complex variable theory . The curves C of the present lemma bound a finite domain D containing every point of σ and no point of o ( T ) - o . It is clear ...
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
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