## Linear Operators, Part 1 |

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Results 1-3 of 86

Page 436

Show that if 3 contains a non-void T-open bounded (II.1.7) set, then 3: must be

finite dimensional. 6 Let 3: be a B-space, and 3., a

** topology of 3:1 is the same as the relative 3" topology of 3:1. 7 Let 3: be a

linear ...

Show that if 3 contains a non-void T-open bounded (II.1.7) set, then 3: must be

finite dimensional. 6 Let 3: be a B-space, and 3., a

**subspace**of 3. Show that the** topology of 3:1 is the same as the relative 3" topology of 3:1. 7 Let 3: be a

linear ...

Page 504

Then there exists a closed separable

m, n = 1, 2, ..., belong to 3 and satisfy the relations ran = 1 and a' (ann) = ( - }) |r.

Then there exists a closed separable

**subspace**) of t such that J is equivalent to a**subspace**of Ş)*. PRoof. Let {ai} be a countable dense subset of Jo, and let {ran),m, n = 1, 2, ..., belong to 3 and satisfy the relations ran = 1 and a' (ann) = ( - }) |r.

Page 513

then U has a continuous inverse. 16 If \) is a closed

Qt is a finite dimensional

a closed

.

then U has a continuous inverse. 16 If \) is a closed

**subspace**of a B-space andQt is a finite dimensional

**subspace**, then \) (P 92 is a closed**subspace**. If \) B J isa closed

**subspace**, and 97 is finite dimensional, it does not follow that \) is closed.

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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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