## 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 ...

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 ...

Page 685

The

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

infinite interval o St . 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 o St . It was observed in Lemma 1 . 3 that a strongly measurable

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

Then there is an absolute constant Cx , which is independent of the

and independent of j , such that ule ... The symbol CPR will be used for Cx with

the additional hypothesis that the operators in the

Then there is an absolute constant Cx , which is independent of the

**semigroup**and independent of j , such that ule ... The symbol CPR will be used for Cx with

the additional hypothesis that the operators in the

**semi**-**group**are positive and ...### What people are saying - Write a review

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### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

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