## Linear Operators: Spectral operators |

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Page 1989

The basic

The basic

**spectral measure**e on which is used to define the algebras A and AP is defined in terms of the Fourier transform F on H by the equation ( 15 ) e ( o ) = F- ? ( 0 ) F , σε Σ , , where ulo ) is the multiplication projection ...Page 2107

**Spectral measures**, locally convex spaces and order .**Spectral measures**have been studied in connection with ( partially ) ordered spaces by Schaefer [ 7 , 10 , 11 ) , Schaefer and Walsh [ 1 ] , and Walsh [ 1 , 2 , 3 ) .Page 2110

One of the most surprising results due to Walsh [ 2 ] is the result that if u is an equicontinuous Borel

One of the most surprising results due to Walsh [ 2 ] is the result that if u is an equicontinuous Borel

**spectral measure**into the space of continuous operators in a space E in which closed bounded sets are compact ( for example ...### 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 | |

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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