## Linear Operators: General theory |

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Page 614

Throughout this section , X will denote a complex B - space , and { T ( t ) } a

strongly continuous

satisfying the conditions of the following definition . 1 DEFINITION . A family { T ( t

) } , 0 < t ...

Throughout this section , X will denote a complex B - space , and { T ( t ) } a

strongly continuous

**semi**-**group**of operators in x ; i.e. , a family of operatorssatisfying the conditions of the following definition . 1 DEFINITION . A family { T ( t

) } , 0 < t ...

Page 685

The

function T ( ) x is measurable , with respect to Lebesgue measure , on the infinite

interval 0 < t . It was observed in Lemma 1.3 that a strongly measurable

The

**semi**-**group**is said to be strongly measurable if , for each x in X , thefunction T ( ) x is measurable , with respect to Lebesgue measure , on the infinite

interval 0 < t . It was observed in Lemma 1.3 that a strongly measurable

**semi**-**group**is ...Page 697

Nelson Dunford, Jacob T. Schwartz, William G. Bade. 11 LEMMA . Let ( S , E , u )

be a positive measure space and let { T ( 4 , ... , tx ) , 41 , ... , tx > 0 } be a strongly

measurable

Nelson Dunford, Jacob T. Schwartz, William G. Bade. 11 LEMMA . Let ( S , E , u )

be a positive measure space and let { T ( 4 , ... , tx ) , 41 , ... , tx > 0 } be a strongly

measurable

**semi**-**group**of operators in L ( S , E , u ) with T ( tj , ... , tx ) , 51 , \ T ...### What people are saying - Write a review

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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