## Linear operators: Spectral operators |

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Page 2107

spaces by Schaefer [7, 10, 11], Schaefer and Walsh [1], and Walsh [1, 2, 3]. We

shall give a condensed description of some of this work, but, in order to be brief, it

is ...

**Spectral measures**have been studied in connection with (partially) orderedspaces by Schaefer [7, 10, 11], Schaefer and Walsh [1], and Walsh [1, 2, 3]. We

shall give a condensed description of some of this work, but, in order to be brief, it

is ...

Page 2110

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

equicontinuous Borel

a space E in which closed bounded sets are compact (for example, a Montel

space), ...

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

equicontinuous Borel

**spectral measure**into the space of continuous operators ina space E in which closed bounded sets are compact (for example, a Montel

space), ...

Page 2143

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

unique

<j(x) s 8, = 0, 8 e £f{T), a(x) g 8'. This

Let Tbea 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(8)x = x, 8 e Sf{T),<j(x) s 8, = 0, 8 e £f{T), a(x) g 8'. This

**spectral measure**is bounded, is countably ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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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