## Linear Operators: General theory |

### From inside the book

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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 49

The Principle of Uniform Boundedness Throughout, the text, all linear vector

spaces will be over the field of real or the field of

space is one for which the field 0 is the set of real numbers; a complex vector

space ...

The Principle of Uniform Boundedness Throughout, the text, all linear vector

spaces will be over the field of real or the field of

**complex numbers**. A real vectorspace is one for which the field 0 is the set of real numbers; a complex vector

space ...

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 ...### What people are saying - Write a review

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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 closed linear manifold compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive Definition denote dense differential equations Doklady Akad element equivalent everywhere exists extended real valued extension fi(E finite dimensional finite number function f Hausdorff space Hence Hilbert space homeomorphism inequality integral interval Lebesgue measure Lemma linear functional linear map linear operator linear topological space LP(S measurable function 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 Russian scalar semi-group sequentially compact Show simple functions subset subspace Suppose theory topological space uniformly unique v(fi valued function Vber vector valued weakly compact zero