## Linear Operators: Spectral operators |

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They show that if T is spectral , then T * has a

They show that if T is spectral , then T * has a

**unique**resolution of the identity of class ( X ) ; moreover , if T * is spectral of class ( T ) where I $ x ...Page 2143

Let T be a bounded linear operator in the complex B - space X. Then there is a

Let T be a bounded linear operator in the complex B - space X. Then there is a

**unique**spectral measure on the field S ( T ) with the properties E ( S ) = x ...Page 2265

... Vam ( Ec ) for each family { Ex } $ D for which V & E , E D. Then there is a

... Vam ( Ec ) for each family { Ex } $ D for which V & E , E D. Then there is a

**unique**multiplicity function on B which is an extension of m on D. Proof .### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

32 other sections not shown

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