## 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

Spectra] Theory in a Finite Dimensional Space Throughout this section, X will

denote a finite dimensional complex ... The spectrum a(T) of an operator T in a

finite dimensional fi-space is the set of

...

Spectra] Theory in a Finite Dimensional Space Throughout this section, X will

denote a finite dimensional complex ... The spectrum a(T) of an operator T in a

finite dimensional fi-space is the set of

**complex numbers**A such that A/ — T is not...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries 84 | 34 |

Copyright | |

44 other sections not shown

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### Common terms and phrases

Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers contains continuous functions convex set Corollary countably additive Definition denote dense differential equations Doklady Akad Duke Math element equivalent exists finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lemma 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 properties proved real numbers reflexive Riesz Russian scalar semi-group sequentially compact Show simple functions subset subspace Suppose theory TM(S topological space Trans valued function Vber vector space weak topology weakly compact weakly sequentially compact zero