Linear Operators: Spectral operators |
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Page 1931
If the domain of a countably additive spectral measure E is a o - field , then E is countably additive in the strong operator topology and bounded . The boundedness of E ( o ) follows from Corollaries IV.10.2 and II.3.21 .
If the domain of a countably additive spectral measure E is a o - field , then E is countably additive in the strong operator topology and bounded . The boundedness of E ( o ) follows from Corollaries IV.10.2 and II.3.21 .
Page 2087
68 Let As be the operator of the preceding exercise and let B be an arbitrary bounded linear operator in Hp . Then ( i ) The operator As + B with domain ( p ) T ( 29 ) ( RN ) is the infinitesimal generator of a strongly continuous semi ...
68 Let As be the operator of the preceding exercise and let B be an arbitrary bounded linear operator in Hp . Then ( i ) The operator As + B with domain ( p ) T ( 29 ) ( RN ) is the infinitesimal generator of a strongly continuous semi ...
Page 2256
where C , is a finite collection of closed Jordan curves bounding a domain D , containing the union of o ( T ) and a neighborhood of infinity , C , being oriented in the customary positive sense of complex variable theory .
where C , is a finite collection of closed Jordan curves bounding a domain D , containing the union of o ( T ) and a neighborhood of infinity , C , being oriented in the customary positive sense of complex variable theory .
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Contents
SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1931 |
Copyright | |
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adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero