## Linear Operators, Part 1 |

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Page 91

However, Kolmogoroff [1] proved that a topological linear space is

convex neighborhood of the origin. Wehausen [1] showed that if a topological

linear space has a ...

However, Kolmogoroff [1] proved that a topological linear space is

**homeomorphic**to a normed linear space if and only if there exists a boundedconvex neighborhood of the origin. Wehausen [1] showed that if a topological

linear space has a ...

Page 157

Thus the map E → Ze may be regarded as a

subset of M(S, X, u). It is clear that this

into Cauchy sequences. Thus if g(E, E,) → 0, there is, by Corollary 6.5, a function

z ...

Thus the map E → Ze may be regarded as a

**homeomorphism**of 2(u) onto asubset of M(S, X, u). It is clear that this

**homeomorphism**maps Cauchy sequencesinto Cauchy sequences. Thus if g(E, E,) → 0, there is, by Corollary 6.5, a function

z ...

Page 442

If Q is a compact Hausdorff space, and C(Q) is the B-space of all real or compler

continuous functions on Q, then the mapping A : q → a of Q into a subset Q of the

ertremal points of S* is a

If Q is a compact Hausdorff space, and C(Q) is the B-space of all real or compler

continuous functions on Q, then the mapping A : q → a of Q into a subset Q of the

ertremal points of S* is a

**homeomorphism**where C*(Q) has its C(Q) topology.### What people are saying - Write a review

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### Contents

A Settheoretic Preliminaries | 1 |

Convergence and Uniform Convergence of Generalized | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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### Common terms and phrases

additive set function algebra Amer analytic arbitrary B-space Banach baſs Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complete complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense differential Doklady Akad element equation equivalent exists finite dimensional function defined function f g-field g-finite Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lebesgue measure Lemma Let f lim ſº linear map linear operator linear topological space Lp(S Math measurable functions measure space metric space Nauk SSSR N.S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc properties proved real numbers Riesz scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact zero