## Linear Operators, Part 1 |

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Page 483

If T is

is compact and hence closed in the })* topology of Q)**. Thus if T is

If T is

**weakly compact**, then TS is compact in the Q)* topology of 9) and thus x(TS)is compact and hence closed in the })* topology of Q)**. Thus if T is

**weakly****compact**, (i) yields T**(s) g ×(TS). According to Theorem V.4.5, S, - S**, and so ...Page 484

Linear combinations of

product of a

let T, ...

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, U e B(£, Q)), We B(), 3), Ve B(3, 3'), x, 3 e q), andlet T, ...

Page 507

Let (S, 2, u) be a g-finite positive measure space, and let T be a

operator on L1(S, X, u) to a separable subset of the B-space 3. Then there exists

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

Let (S, 2, u) be a g-finite positive measure space, and let T be a

**weakly compact**operator on L1(S, X, u) to a separable subset of the B-space 3. Then there exists

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

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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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