## Linear operators: Spectral operators |

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Page 1930

3 Definition. A spectral measure E is said to be countably additive if for each x* in

X* and each x in X the scalar set function x*E(-)x is countably additive on the

Spectral ...

3 Definition. A spectral measure E is said to be countably additive if for each x* in

X* and each x in X the scalar set function x*E(-)x is countably additive on the

**domain**of E. -*• 4 Corollary. If the**domain**of a countably additive 1930 xv.Spectral ...

Page 2087

(69) Let Aq and B be as in the preceding exercise and let D = (djk) be a formal

differential operator on <PP whose elements are polynomials with constant

coefficients and of degrees at most 2q — 2. Then (i) The

natural ...

(69) Let Aq and B be as in the preceding exercise and let D = (djk) be a formal

differential operator on <PP whose elements are polynomials with constant

coefficients and of degrees at most 2q — 2. Then (i) The

**domain**D(DS) of thenatural ...

Page 2256

where Cx is a finite collection of closed Jordan curves bounding a

containing the union of a(T) and a neighborhood of infinity, G1 being oriented in

the customary positive sense of complex variable theory. The curves C of the ...

where Cx is a finite collection of closed Jordan curves bounding a

**domain**£>!containing the union of a(T) and a neighborhood of infinity, G1 being oriented in

the customary positive sense of complex variable theory. The curves C of the ...

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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