## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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Results 1-3 of 37

Page 1935

complex plane , o ( E ( 81 ) x ) is void . By the preceding corollary , then E ( 81 ) x

= 0 . ... o ( Ax ) 5 0 ( x ) for every x in X . PROOF . Let 8 , 8 , be disjoint closed sets

of

complex plane , o ( E ( 81 ) x ) is void . By the preceding corollary , then E ( 81 ) x

= 0 . ... o ( Ax ) 5 0 ( x ) for every x in X . PROOF . Let 8 , 8 , be disjoint closed sets

of

**complex numbers**and let E be a resolution of the identity for T . Since ( EI ...Page 1955

Let A be a bounded linear operator in X . The point spectrum of A is the set o ( A )

consisting of all

continuous spectrum of A is the set oc ( A ) of

is ...

Let A be a bounded linear operator in X . The point spectrum of A is the set o ( A )

consisting of all

**complex numbers**, for which XI – A is not one - to - one . Thecontinuous spectrum of A is the set oc ( A ) of

**complex numbers**, for which XI – Ais ...

Page 2171

The symbol T is a bounded linear operator on a complex B - space X . For each x

in X the symbol [ x ] will be used for the closed linear manifold determined by all

the vectors RTÉ ; T ' ) x with & in p ( T ) . If o is a closed set of

The symbol T is a bounded linear operator on a complex B - space X . For each x

in X the symbol [ x ] will be used for the closed linear manifold determined by all

the vectors RTÉ ; T ' ) x with & in p ( T ) . If o is a closed set of

**complex numbers**...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

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### Common terms and phrases

analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear clearly closure commuting compact complex consider constant contained converges Corollary corresponding countably additive defined Definition denote dense determined differential operator 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 positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum statement strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero