## Linear Operators: Spectral operators |

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Page 2125

( 8 ) / 8 € D ( P ) } and { P ( 8 ) * 18 € D ( P ) } are total on H . It is proved that every

g . s . m . can be extended to a class Do ( P ) of Borel subsets of C which is ...

**Borel sets**and if X , Y EH , then ( P ( 8 ) x , y ) = 2 ( P ( 8x ] a , y ) . ( iv ) The sets { P( 8 ) / 8 € D ( P ) } and { P ( 8 ) * 18 € D ( P ) } are total on H . It is proved that every

g . s . m . can be extended to a class Do ( P ) of Borel subsets of C which is ...

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4 that there is a spectral measure A in X * defined on the

that xT ( ) z * = 5 ( A ) xA ( da ) x * ... It will now be shown that , because of the

completeness of B , the operator A ( e ) is , for every

4 that there is a spectral measure A in X * defined on the

**Borel sets**in 1 and suchthat xT ( ) z * = 5 ( A ) xA ( da ) x * ... It will now be shown that , because of the

completeness of B , the operator A ( e ) is , for every

**Borel set**e , the adjoint of a ...Page 2233

Let T be a spectral operator with resolution of the identity E , and let f be a

function analytic in an open set U such that E ( U ) ... The operator f ( T ) of

Definition 8 is closed , linear , and independent of the particular sequence of

Let T be a spectral operator with resolution of the identity E , and let f be a

function analytic in an open set U such that E ( U ) ... The operator f ( T ) of

Definition 8 is closed , linear , and independent of the particular sequence of

**Borel sets**used to ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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adjoint operator analytic applications arbitrary assumed B-space Banach space belongs Boolean algebra Borel sets boundary bounded bounded operator Chapter clear closed commuting compact complex condition consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined domain elements equation equivalent established example exists extension fact finite follows formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm normal perturbation plane positive preceding present problem projections PROOF properties proved range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero