## Linear Operators: Spectral operators |

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Page 1945

The central result in this direction is a theorem of Wermer which states that every

scalar type

theorem and other special properties of spectral

The central result in this direction is a theorem of Wermer which states that every

scalar type

**operator in Hilbert**space is equivalent to a normal operator. Thistheorem and other special properties of spectral

**operators in Hilbert**space are ...Page 1947

BTB1 = B-1(T*)~lB = {(BTB-1)*)-1, which proves that BTB'1 is a unitary

Q.E.D. 2 Lemma. Let 93^ . . . , 93k be a finite collection of commuting bounded

Boolean algebras of projections in a

bounded ...

BTB1 = B-1(T*)~lB = {(BTB-1)*)-1, which proves that BTB'1 is a unitary

**operator**.Q.E.D. 2 Lemma. Let 93^ . . . , 93k be a finite collection of commuting bounded

Boolean algebras of projections in a

**Hilbert**space §. Then tliere exists abounded ...

Page 2538

On the distribution of the spectra of normal

Japan Acad. 37, 464-468 (1961). Simplification of the canonical spectral

representation of a normal

Fac. Educ.

On the distribution of the spectra of normal

**operators in Hilbert**spaces. Proc.Japan Acad. 37, 464-468 (1961). Simplification of the canonical spectral

representation of a normal

**operator in Hilbert**space and its applications. Mem.Fac. Educ.

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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 bounded spectral commuting compact complex numbers complex plane constant contains continuous functions converges Corollary countably additive Definition denote differential operator disjoint Doklady Akad domain eigenvalues elements equation equivalent exists finite number Foias follows from Lemma follows from Theorem formal differential operator formula Hence Hilbert space hypothesis identity inequality inverse Lebesgue Math matrix multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial preceding 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