## Linear Operators: General theory |

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Page 3

We presuppose a familiarity with the real and

extended real number system we mean the real numbers with the symbols +oo

and — oo adjoined; by the extended

We presuppose a familiarity with the real and

**complex number**systems. By theextended real number system we mean the real numbers with the symbols +oo

and — oo adjoined; by the extended

**complex number**system we mean the ...Page 238

During the course of the investigation a

of the spaces to be considered and ... With the one exception of Hilbert space,

each of them will consist of real or

During the course of the investigation a

**number**of interesting special propertiesof the spaces to be considered and ... With the one exception of Hilbert space,

each of them will consist of real or

**complex**valued functions /, g defined on a ...Page 556

The spectrum a(T) of an operator T in a finite dimensional fi-space is the set of

...

The spectrum a(T) of an operator T in a finite dimensional fi-space is the set of

**complex numbers**X such that XI — T is not one-to-one. The index v(X) of a**complex number**X is the smallest non-negative integer v such that (XI — T)"x = 0...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

79 other sections not shown

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### Common terms and phrases

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