## Linear Operators: Spectral operators |

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Page 2403

... proof amounts merely to an application of the Hölder inequality and the Riesz

convexity theorem . 5 LEMMA . Let X be a B - space , and let ( S , E ,

finite measure space . Let 1 Spass 00. Let A ( :, :) be a strongly

...

... proof amounts merely to an application of the Hölder inequality and the Riesz

convexity theorem . 5 LEMMA . Let X be a B - space , and let ( S , E ,

**u**) be a o -finite measure space . Let 1 Spass 00. Let A ( :, :) be a strongly

**u**Xu -**measurable**...

Page 2404

Moreover , the mapping ( 12 ) $ ( ) -S41 Al · , t ) f ( t )

mapping in L ( S , M , X ) , having norm at most max [ { A } , { A } , ] . Proof . We first

observe that if f is p -

...

Moreover , the mapping ( 12 ) $ ( ) -S41 Al · , t ) f ( t )

**u**( dt ) is a bounded linearmapping in L ( S , M , X ) , having norm at most max [ { A } , { A } , ] . Proof . We first

observe that if f is p -

**measurable**, the function A ( s , t ) f ( t ) is a u x -**measurable**...

Page 2466

Put u = v + d . Let H ' denote the set of all sequences f = { ft ( ) } of

functions defined on R such that ( 33 ) \ f12 = Š S 15+ ( a ) 2 ( da ) < oo . The set H

' is a complete Hilbert space with the inner product do ( 34 ) ( 5 , ģ ) = Ë S fo ( a ) ...

Put u = v + d . Let H ' denote the set of all sequences f = { ft ( ) } of

**u**-**measurable**functions defined on R such that ( 33 ) \ f12 = Š S 15+ ( a ) 2 ( da ) < oo . The set H

' is a complete Hilbert space with the inner product do ( 34 ) ( 5 , ģ ) = Ë S fo ( a ) ...

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

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