## Linear Operators: Spectral theory |

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Page 1036

Then the infinite product Pa ( T ) = T ( 1 I ( - ) av

Then the infinite product Pa ( T ) = T ( 1 I ( - ) av

**converges**and defines a function analytic for 1 + 0 . For each fixed 1 # 0 , P ( T ) is a continuous complex valued function on the B - space of all Hilbert - Schmidt operators .Page 1436

Let { en } be a bounded sequence of elements of D ( T ) such that { Tgn }

Let { en } be a bounded sequence of elements of D ( T ) such that { Tgn }

**converges**. Find a subsequence { gn ; } = { h ; } such that x * ( h ; )**converges**for each 1 , 1 si sk . Then ħ ; = h ; - -1x * ( h ; ) ; is in D , and Tħ ...Page 1664

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

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 1 , ( C ) that it suffices to show that ( pil · * q ( x ) dx Pilis LEA LEA**converges**...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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