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 2107
... spectral ( respectively , scalar type ) operator , then T is spectral ... measure μ on X to A we mean a mapping 8 → μ ( 8 ) from the Baire field Bo ... spectral measures with continuous homomorphisms of C ( X ) into A , thus affording an ...
... spectral ( respectively , scalar type ) operator , then T is spectral ... measure μ on X to A we mean a mapping 8 → μ ( 8 ) from the Baire field Bo ... spectral measures with continuous homomorphisms of C ( X ) into A , thus affording an ...
Page 2110
... measure into the space of con- μ tinuous operators in a space E in which ... spectral operators . Questions concerning the inter- polation of spectral operators and their resolutions of ... spectral operator 2110 XV.16 XV . SPECTRAL OPERATORS.
... measure into the space of con- μ tinuous operators in a space E in which ... spectral operators . Questions concerning the inter- polation of spectral operators and their resolutions of ... spectral operator 2110 XV.16 XV . SPECTRAL OPERATORS.
Page 2143
... spectral measure on the field properties ( T ) with the E ( 8 ) x = x , de S ( T ) , σ ( x ) = 8 , = 0 , d = S ( T ) , σ ( x ) ≤ d ' . This spectral measure is bounded , is countably additive on S ( T ) , and com- mutes with T. PROOF ...
... spectral measure on the field properties ( T ) with the E ( 8 ) x = x , de S ( T ) , σ ( x ) = 8 , = 0 , d = S ( T ) , σ ( x ) ≤ d ' . This spectral measure is bounded , is countably additive on S ( T ) , and com- mutes with T. PROOF ...
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
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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