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 2125
... Borel subsets of C which is maximal ( in a certain sense ) and that such an extension is uniquely determined . In fact , let Do ( P ) consist of the set of all Borel sets 8C such that sup { | P ( o ) || σ € D ( P ) , o ≤ 8 } < + ...
... Borel subsets of C which is maximal ( in a certain sense ) and that such an extension is uniquely determined . In fact , let Do ( P ) consist of the set of all Borel sets 8C such that sup { | P ( o ) || σ € D ( P ) , o ≤ 8 } < + ...
Page 2202
... set A of maximal ideals , and any homeomorphic isomorphism T between these algebras uniquely determines a regular countably additive spectral measure E in x defined on the family of Borel sets in A and such that T ( ƒ ) = ƒ ƒ ( \ ) E ...
... set A of maximal ideals , and any homeomorphic isomorphism T between these algebras uniquely determines a regular countably additive spectral measure E in x defined on the family of Borel sets in A and such that T ( ƒ ) = ƒ ƒ ( \ ) E ...
Page 2233
... set U such that E ( U ) I. Let { e } be an arbitrary increasing sequence of bounded Borel sets with closures contained in U , such that E ( = 1 en ) = I. The operator f ( T ) is defined by the equations D ( ƒ ( T ) ) = { x | lim ƒ ( T ...
... set U such that E ( U ) I. Let { e } be an arbitrary increasing sequence of bounded Borel sets with closures contained in U , such that E ( = 1 en ) = I. The operator f ( T ) is defined by the equations D ( ƒ ( T ) ) = { x | lim ƒ ( T ...
Contents
SPECTRAL OPERATORS | 1924 |
An Operational Calculus for Bounded Spectral | 1941 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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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 inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR norm normal operators operators in Hilbert perturbation polynomial Proc PROOF properties prove Pure Appl quasi-nilpotent resolution Russian S₁ 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