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

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Page 2154

( G ) The spectrum

Moreover , there is an integer valued function v defined on lo such that for every

do in to , lado ) " ( 10 ) R ( ) ;

this ...

( G ) The spectrum

**of T**is contained in the rectifiable Jordan curve**T**' o .Moreover , there is an integer valued function v defined on lo such that for every

do in to , lado ) " ( 10 ) R ( ) ;

**T**' ) | , # do , de 420 . In the analysis to follow , it isthis ...

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7 that y is in S (

Lemma 3 . 9 every subset of plT ' ) is in S (

Thus , since o (

...

7 that y is in S (

**T**' ) . It follows that every Borel subset of To is measurable**T**. ByLemma 3 . 9 every subset of plT ' ) is in S (

**T**) and hence in a set measurable**T**.Thus , since o (

**T**) çlo , every Borel set in the plane is measurable**T**. Q . E . D . In...

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subsequence weakly convergent to an element y of X ( cf . Theorem II . 3 . 28 ) .

By replacing the sequence { an } by a suitably chosen subsequence , it may

therefore be assumed that , in the weak topology , we have lim ( ^ n - 10 ) R ( An ;

subsequence weakly convergent to an element y of X ( cf . Theorem II . 3 . 28 ) .

By replacing the sequence { an } by a suitably chosen subsequence , it may

therefore be assumed that , in the weak topology , we have lim ( ^ n - 10 ) R ( An ;

**T**) x ...### 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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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