## Linear Operators, Part 1 |

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Page 483

The symbols S , S ** will be used for the closed unit spheres in X , X ** ,

,

S ) CT ...

The symbols S , S ** will be used for the closed unit spheres in X , X ** ,

**respectively**. Note that T ** is continuous with the X * , Y * topologies in X ** , Y **,

**respectively**( cf. 2.3 ) . Hence , since T ** is an extension of T ( cf. 2.6 ) , ( i ) T ** (S ) CT ...

Page 484

We have already observed ( 2.3 ) that the adjoint T * of any T in B ( x , y ) is

continuous relative to the X , Y topologies in X * , Y * ,

result shows that , if T ' is weakly compact , its adjoint T * has a stronger continuity

...

We have already observed ( 2.3 ) that the adjoint T * of any T in B ( x , y ) is

continuous relative to the X , Y topologies in X * , Y * ,

**respectively**. The followingresult shows that , if T ' is weakly compact , its adjoint T * has a stronger continuity

...

Page 485

Conversely , if T * is weakly compact , it follows from Lemma 7 that T ** is

continuous relative to the X * , Y *** topologies in X ** , Y ** ,

** are the closed unit spheres in X , X ** ,

embedding ...

Conversely , if T * is weakly compact , it follows from Lemma 7 that T ** is

continuous relative to the X * , Y *** topologies in X ** , Y ** ,

**respectively**. If S , S** are the closed unit spheres in X , X ** ,

**respectively**, and if x is the naturalembedding ...

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

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