## Linear Operators: Spectral operators |

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Page 2244

Let S be a set, E a a-field of subsets of S, and E a strongly countably additive

resolution of the identity defined on E.

on S. Then the operator T(f) of Definition 10 is a scalar type spectral operator,

whose ...

Let S be a set, E a a-field of subsets of S, and E a strongly countably additive

resolution of the identity defined on E.

**Let f**be a E-measurable function definedon S. Then the operator T(f) of Definition 10 is a scalar type spectral operator,

whose ...

Page 2248

Let T be a spectral operator, and E its resolution of identity.

analytic in a domain U which, when taken together with a finite number of

exceptional points p, includes a neighborhood of o(T) and a neighborhood of the

point at ...

Let T be a spectral operator, and E its resolution of identity.

**Let f**be a functionanalytic in a domain U which, when taken together with a finite number of

exceptional points p, includes a neighborhood of o(T) and a neighborhood of the

point at ...

Page 2424

16 Lemma. Let fybea Hilbert space, and let £(§) be the B-space of all bounded

operators in §. Let y and j3 be two real numbers, with y > 0 and 1>]8>0. Let A e'

Hy_g(B(9))), and

variable ...

16 Lemma. Let fybea Hilbert space, and let £(§) be the B-space of all bounded

operators in §. Let y and j3 be two real numbers, with y > 0 and 1>]8>0. Let A e'

Hy_g(B(9))), and

**let f**be an infinitely differentiate ^-valued function of a realvariable ...

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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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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