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 1945
... Bounded Spectral Operators in Hilbert Space What is the relationship between the bounded spectral operators in a Hilbert space H and the bounded normal operators in ? The central result in this direction is a theorem of Wermer which ...
... Bounded Spectral Operators in Hilbert Space What is the relationship between the bounded spectral operators in a Hilbert space H and the bounded normal operators in ? The central result in this direction is a theorem of Wermer which ...
Page 2169
... bounded Borel functions , note that for a fixed continuous function g the set of all bounded Borel functions ƒ for ... spectral measure which , in view of the Orlicz - Pettis Theorem IV.10.1 , is countably additive in the strong operator ...
... bounded Borel functions , note that for a fixed continuous function g the set of all bounded Borel functions ƒ for ... spectral measure which , in view of the Orlicz - Pettis Theorem IV.10.1 , is countably additive in the strong operator ...
Page 2228
... bounded ; E ( o ) D ( T ) ≤ D ( T ) TE ( o ) x = E ( o ) Tx , x = D ( T ) , σ EB ; ( iii ) the restriction T | E ( o ) X with domain D ( T ) ~ E ( σ ) X has its ... spectral operator with 2228 XVIII.2.1 XVIII . UNBOUNDED SPECTRAL OPERATORS.
... bounded ; E ( o ) D ( T ) ≤ D ( T ) TE ( o ) x = E ( o ) Tx , x = D ( T ) , σ EB ; ( iii ) the restriction T | E ( o ) X with domain D ( T ) ~ E ( σ ) X has its ... spectral operator with 2228 XVIII.2.1 XVIII . UNBOUNDED SPECTRAL OPERATORS.
Contents
SPECTRAL OPERATORS | 1924 |
The Spectrum of a Spectral Operator | 1955 |
The Algebras A and | 1966 |
Copyright | |
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A₁ Acad adjoint operator algebra of projections Amer analytic arbitrary B-algebra B-space 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 dense differential operator Dokl Doklady Akad eigenvalues elements equation exists formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis ibid identity inequality invariant subspaces inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR nonselfadjoint norm normal operators operators in Hilbert perturbation Proc PROOF properties prove Pures Appl quasi-nilpotent resolution Russian satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose topology trace class type spectral operator unbounded uniformly bounded vector zero