## Linear Operators: Spectral operators |

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Page 2011

For every set o in E and every such matrix Â ( s ) we

For every set o in E and every such matrix Â ( s ) we

**define**the matrix ( 1 ) ... for such sets o the operator Â , is a bounded everywhere**defined**operator .Page 2018

For a closed operator As the resolvent set P ( As ) has been

For a closed operator As the resolvent set P ( As ) has been

**defined**( see Section VII.9 ) as the set of all complex numbers for which ( I – As ) -1 exists ...Page 2284

x ;, now

x ;, now

**defined**on the Borel sets of the plane P are positive and vanish outside en . Moreover , there is a natural continuous linear map Tn of EnX into ...### 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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### Common terms and phrases

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