## Linear Operators, Part 1 |

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Page 161

Hence u, -> u, which proves that

to Lemma 1.5, sup u(E) < v(u, S) < 4 sup u(E). Eel' Eel This shows that v(u, S) is a

...

Hence u, -> u, which proves that

**bass**, 2, 3) is complete. It follows, therefore, that**bass**, X, t) is a B-space. If t is the set of real or complex numbers, then accordingto Lemma 1.5, sup u(E) < v(u, S) < 4 sup u(E). Eel' Eel This shows that v(u, S) is a

...

Page 314

Q.E.D. 12 THEOREM. A subset K of

and only if there exists a non-negative u in

0 uniformly for Že K. PRoof. Let K C

...

Q.E.D. 12 THEOREM. A subset K of

**bass**, 2) is weakly sequentially compact ifand only if there exists a non-negative u in

**bass**, 2) such that lim Å(E) = 0 a(E)—-0 uniformly for Že K. PRoof. Let K C

**bass**, 2) be weakly sequentially compact and...

Page 340

Then there is a u e

only if {A,B} is bounded and the limit lim u,(E) exists for every set E e 2. ra 19 Let

u be a non-negative element of

Then there is a u e

**bass**, 2) such that lims, f(s)...(b) = s.ss),(ds), fe B(S, 2) if andonly if {A,B} is bounded and the limit lim u,(E) exists for every set E e 2. ra 19 Let

u be a non-negative element of

**bass**, 2) and let**bass**, 2.(1) be the subspace of ...### 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 | |

27 other sections not shown

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