## Linear operators: Spectral operators |

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Page 2094

12) that if J is a weakly complete B-space, then any prespectral

automatically

and Dowson [1] have considered prespectral

obtained ...

12) that if J is a weakly complete B-space, then any prespectral

**operator**isautomatically

**spectral**, and so has a unique resolution of the identity. Berksonand Dowson [1] have considered prespectral

**operators**in some detail and haveobtained ...

Page 2118

A generalized scalar

scalar

...

A generalized scalar

**operator**T e B(X) is said to be regular if it has a regular**spectral**distribution. Although it is not known whether or not every generalizedscalar

**operator**is regular (unless the**spectrum**is sufficiently "thin"), given any two...

Page 2228

Unbounded

subsets of the complex plane. Let T be a Unear operator whose domain and

range are contained in a complex .B-space 3E. Then T is said to be a

Unbounded

**Spectral Operators**1 Definition. Let ^ denote the a-field of Borelsubsets of the complex plane. Let T be a Unear operator whose domain and

range are contained in a complex .B-space 3E. Then T is said to be a

**spectral****operator**if ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

47 other sections not shown

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### Common terms and phrases

adjoint operator algebra of projections Amer analytic arbitrary asymptotic B-space Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complex numbers complex plane constant contains continuous functions converges Corollary countably additive Definition denote dense differential operator disjoint Doklady Akad domain eigenvalues elements equation exists finite number Foias follows from Lemma follows from Theorem formal differential operator formula Hence Hilbert space hypothesis identity inequality inverse Lebesgue Math matrix measurable functions multiplicity Nauk SSSR norm normal operators operators in Hilbert perturbation polynomial Proof properties prove quasi-nilpotent restriction Russian satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset Suppose trace class type spectral operator unbounded uniformly bounded unique vector weakly complete zero