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 1912
... respect to a finitely additive set function as well as with respect to a countably additive measure . Thus he need be familiar with only a relatively small part of the contents of Chapter III . He should have a good understanding of the ...
... respect to a finitely additive set function as well as with respect to a countably additive measure . Thus he need be familiar with only a relatively small part of the contents of Chapter III . He should have a good understanding of the ...
Page 1942
... respect to § in any closed set p contained in p ( T ) . - -n PROOF . For έ in p the function ( § — λ ) − " is bounded on σ ( T ) , so that the integral exists . Moreover , E ( dλ ) JESP + ( E ) . ( § — λ ) n + 1 ≤ ph + 1v ( E ) ...
... respect to § in any closed set p contained in p ( T ) . - -n PROOF . For έ in p the function ( § — λ ) − " is bounded on σ ( T ) , so that the integral exists . Moreover , E ( dλ ) JESP + ( E ) . ( § — λ ) n + 1 ≤ ph + 1v ( E ) ...
Page 2104
... respect to one consistent semi - inner product , it has a real numerical range with respect to all . Lumer called such operators Hermitian operators on X ; he further showed that this 2104 XV.16 XV . SPECTRAL OPERATORS.
... respect to one consistent semi - inner product , it has a real numerical range with respect to all . Lumer called such operators Hermitian operators on X ; he further showed that this 2104 XV.16 XV . SPECTRAL OPERATORS.
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
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 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