## Linear Operators, Part 2 |

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Page 1036

Then the infinite product WAT ) = ( 1 - 1 ) và

analytic for 2 + 0 . For each fixed à # 0 , ( T ) is a continuous complex valued

function on the B - space of all Hilbert - Schmidt operators . Proof . First note that if

& is a ...

Then the infinite product WAT ) = ( 1 - 1 ) và

**converges**and defines a functionanalytic for 2 + 0 . For each fixed à # 0 , ( T ) is a continuous complex valued

function on the B - space of all Hilbert - Schmidt operators . Proof . First note that if

& is a ...

Page 1420

Indeed , let { { n } be a sequence in D ( T1 ( T ) ) . Suppose that { n }

zero in the topology of D ( T1 ( t ) ) . Then , by assumption ( b ) , { { n }

to zero in the topology of D ( T2 ( t + t ' ) ) . Conversely , let { { n }

...

Indeed , let { { n } be a sequence in D ( T1 ( T ) ) . Suppose that { n }

**converges**tozero in the topology of D ( T1 ( t ) ) . Then , by assumption ( b ) , { { n }

**converges**to zero in the topology of D ( T2 ( t + t ' ) ) . Conversely , let { { n }

**converge**to zero...

Page 1664

The Fourier series of an element F in D , ( C )

Proof . It follows from the Definition 37 of the topology in D , ( C ) that it suffices to

show that n ( 29 ' l eil• * Q ( x ) dx JC

q ...

The Fourier series of an element F in D , ( C )

**converges**unconditionally to F .Proof . It follows from the Definition 37 of the topology in D , ( C ) that it suffices to

show that n ( 29 ' l eil• * Q ( x ) dx JC

**converges**unconditionally to F ( q ) for eachq ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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