Linear Operators: Spectral operators |
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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 d≤ С such that sup { | P ( 0 ) || 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 d≤ С such that sup { | P ( 0 ) || 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 ( U - 1 en ) = I. The operator f ( T ) is defined by the equations n D ( ƒ ( T ' ) ) = { x | lim ƒ ...
... 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 ( U - 1 en ) = I. The operator f ( T ) is defined by the equations n D ( ƒ ( T ' ) ) = { x | lim ƒ ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
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A₁ algebra Amer analytic applications arbitrary B-space Banach Banach space Boolean algebra Borel sets boundary bounded Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator Doklady Akad elements equation equivalent established example exists extension finite follows formula function given gives H₁ Hence Hilbert space hypothesis identity integral invariant inverse Lemma limit linear operators Math multiplicity Nauk SSSR norm normal perturbation plane positive preceding present problem Proc projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero