## 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 +co

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 +co

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

for every ...

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 one-to-one. The index v(X) of a**complex number**A is the smallest non-negative integer v such that ()J—T)"x = 0for every ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries 84 | 34 |

Copyright | |

80 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

a-finite 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 continuous linear functional convex set Corollary countably additive Definition denote dense Doklady Akad element equivalent everywhere exists finite dimensional follows from Theorem function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lebesgue measure linear map linear operator linear topological space LP(S measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative non-zero normed linear space 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 valued function vector space weak topology weakly compact weakly sequentially compact zero