## Linear Operators: General theory |

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Page 224

It will be assumed that the reader is familiar with the elementary theory of

applied here to obtain the extensions which will be used later. Throughout this

section.

It will be assumed that the reader is familiar with the elementary theory of

**complex valued**analytic functions of one complex variable and this theory will beapplied here to obtain the extensions which will be used later. Throughout this

section.

Page 238

With the one exception of Hilbert space, each of them will consist of real or

and multiplication are understood to be defined in the natural way, i.e., by the

equations ...

With the one exception of Hilbert space, each of them will consist of real or

**complex valued**functions /, g defined on a specified domain S. Here, additionand multiplication are understood to be defined in the natural way, i.e., by the

equations ...

Page 564

Here A(t) = (aa(t)) is an nxn

variable tel: — oo;Ła<<</?^+oo, and a solution is a

vector y(t) e 22", differentiable and satisfying the differential system for each tel.

The theory ...

Here A(t) = (aa(t)) is an nxn

**complex valued**matrix, continuous in the realvariable tel: — oo;Ła<<</?^+oo, and a solution is a

**complex valued**(column)vector y(t) e 22", differentiable and satisfying the differential system for each tel.

The theory ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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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