Linear Operators, Part 2 |
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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 ( σ ) || 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 ( σ ) || 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 ( \ ) 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 ( \ ) 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 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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 Borel function 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 eigenvalues elements equation exists finite number follows from Lemma 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