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

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Page 2108

143 ] used the word “ spectral ” ) if there

measure u on X to A and a bounded Baire measurable function f : X + C such that

a = s f ( ) u ( dx ) . It follows that there

143 ] used the word “ spectral ” ) if there

**exists**a compact space X , a spectralmeasure u on X to A and a bounded Baire measurable function f : X + C such that

a = s f ( ) u ( dx ) . It follows that there

**exists**a spectral measure va defined on a ...Page 2278

There

for each F * € C * , m ( F * ) is the least cardinal power of a set of cyclic subspaces

spanning F * X * in the X - topology . There is a unique decomposition of the ...

There

**exists**a unique multiplicity function m defined on B * with the property thatfor each F * € C * , m ( F * ) is the least cardinal power of a set of cyclic subspaces

spanning F * X * in the X - topology . There is a unique decomposition of the ...

Page 2405

If he L ; ( S , E , p ) and 2 sr < 00 , it follows that the integral ( Ah ) ( 8 ) = S 14 ( 8 , t

) | h ( ) u ( dt ) ( 14 )

an element f of L ( S , E , u ) , we have Ahl , $ { A } , \ h \ , . Thus , using Theorem ...

If he L ; ( S , E , p ) and 2 sr < 00 , it follows that the integral ( Ah ) ( 8 ) = S 14 ( 8 , t

) | h ( ) u ( dt ) ( 14 )

**exists**for u - almost all s , and that , writing fl . for the norm ofan element f of L ( S , E , u ) , we have Ahl , $ { A } , \ h \ , . Thus , using Theorem ...

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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