## Linear Operators: General theory |

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Page 22

in A has a neighborhood containing at most a

in A has a neighborhood containing at most a

**finite number**of an. Since a**finite****number**of these neighborhoods cover A, the sequence {a„} consists of only a**finite number**of distinct points of A, and therefore most certainly does have a ...Page 200

In order to avoid difficulties which might otherwise arise from the presence of

infinite products such as JJ ,ua(Ła) it is convenient to -ft i assume that for all but a

...

In order to avoid difficulties which might otherwise arise from the presence of

infinite products such as JJ ,ua(Ła) it is convenient to -ft i assume that for all but a

**finite number**of a, fix is non-negative and fta{Sa) = 1. In this case the product JJ is...

Page 579

Every non-zero

such a

given by the formula where v is the order of the pole. Proof. Since a(T) is compact

, the ...

Every non-zero

**number**in a{T) is a pole of T and has**finite**positive index. Forsuch a

**number**X, the projection E(X) has a non-zero**finite**dimensional rangegiven by the formula where v is the order of the pole. Proof. Since a(T) is compact

, the ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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a-field Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence compact operator complex numbers complex valued contains continuous functions continuous linear convex set Corollary countably additive Definition denote dense differential equations disjoint sets Doklady Akad Duke Math element equivalent everywhere exists extended real valued extension finite dimensional finite number function f Hausdorff space Hence Hilbert space homeomorphism inequality interval Lebesgue measure lim sup linear functional linear map linear operator linear topological space LP(S measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space null set open set operator topology positive measure space Proc Proof properties proved real numbers Riesz Russian semi-group sequentially compact Show simple functions subset subspace Suppose theory topological space Trans uniformly unique v(fi valued function Vber vector valued weakly compact