## Linear operators: Spectral operators |

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Page 2127

Nalmark [12] showed that there exists a function A which is analytic in some half-

plane ./(«) > — 17(17 > 0) such that the spectrum of L consists of the interval [0, +

00) together with a

...

Nalmark [12] showed that there exists a function A which is analytic in some half-

plane ./(«) > — 17(17 > 0) such that the spectrum of L consists of the interval [0, +

00) together with a

**finite number**of points Ax An such that Afc = 8% , where J(sk)...

Page 2358

Since 0 is not in a(T) by assumption, there exists a constant K1 such that Since

we have assumed in both cases (a) and (b) that M \A\ tt, < 1 for all but a

function ...

Since 0 is not in a(T) by assumption, there exists a constant K1 such that Since

we have assumed in both cases (a) and (b) that M \A\ tt, < 1 for all but a

**finite****number**of indices i, the inequality (ii) gives us an immediate bound for thefunction ...

Page 2362

Let T be a discrete spectral operator in the reflexive B-space X. Suppose that all

but a

R(X; T);let {V ',} be a sequence of bounded domains covering the entire plane, ...

Let T be a discrete spectral operator in the reflexive B-space X. Suppose that all

but a

**finite number**of the points in o(T) are simple poles of the resolvent functionR(X; T);let {V ',} be a sequence of bounded domains covering the entire plane, ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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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 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