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

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Results 1-3 of 85

Page 1947

Let B1 , . . . , Bk be a finite collection of commuting

projections in a Hilbert space H . Then there exists a

operator B in H with a

a self ...

Let B1 , . . . , Bk be a finite collection of commuting

**bounded**Boolean algebras ofprojections in a Hilbert space H . Then there exists a

**bounded**self adjointoperator B in H with a

**bounded**everywhere defined inverse such that BEB - 1 isa self ...

Page 2239

Since f Xe is a

x is in E ( 7 ) X as well as in E ( e ) X , it follows from the operational calculus for

...

Since f Xe is a

**bounded**function , the operator T ( f Xe ) is a**bounded**operator . Ifx is in E ( 7 ) X as well as in E ( e ) X , it follows from the operational calculus for

**bounded**functions ( cf . XVII . 2 . 10 ) that T ( fxe ) X = T ( fxe ) E ( ē ) x = T ( fXeě )...

Page 2361

Let U , be a sequence of

and suppose that lim - minze ui 1z1 = 00 . Let Vi be the boundary of U , . Let 0 Sv

< l , and put Mi = max lululaul - 1 . NEV i . UEO ( T ) Let do $ ( T ) , and let P be an

...

Let U , be a sequence of

**bounded**domains covering the whole complex plane ,and suppose that lim - minze ui 1z1 = 00 . Let Vi be the boundary of U , . Let 0 Sv

< l , and put Mi = max lululaul - 1 . NEV i . UEO ( T ) Let do $ ( T ) , and let P be an

...

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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