## Linear Operators: General theory |

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Page 484

Linear combinations of

product of a

U be ...

Linear combinations of

**weakly compact**operators are**weakly compact**. Theproduct of a

**weakly compact**linear operator and a bounded linear operator is**weakly compact**. Proof. Let T, ?7eB(£,D), WeB{%S), Ve B(3, X), x,pc<P, and let T,U be ...

Page 494

From IV.10.2 we conclude that T* maps the unit sphere of X* into a conditionally

Theorem 4.8 this implies that T is a

From IV.10.2 we conclude that T* maps the unit sphere of X* into a conditionally

**weakly compact**set of rca(S), and therefore T* is a**weakly compact**operator. ByTheorem 4.8 this implies that T is a

**weakly compact**operator. Q.E.D. 4 Theorem.Page 507

Let (S, E, u) be a o-finite positive measure space, and let T be a

operator on L^S, E, u) to a separable subset of the B-space X. Then there exists a

u-essentially unique bounded measurable function x(-) on S to a weakly ...

Let (S, E, u) be a o-finite positive measure space, and let T be a

**weakly compact**operator on L^S, E, u) to a separable subset of the B-space X. Then there exists a

u-essentially unique bounded measurable function x(-) on S to a weakly ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

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