## Linear Operators: Self Adjoint Operators in Hilbert Space. Spectral theory. Part II |

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Page 949

On the other hand , it has been

isomorphic with C ( S ) , where S is a compact Abelian group , and also ( Lemma

3 ) that the continuous characters of S are of the form eins . By Theorem 1.6 , the

set of ...

On the other hand , it has been

**seen**( Theorem 2 ) that AP is isometric andisomorphic with C ( S ) , where S is a compact Abelian group , and also ( Lemma

3 ) that the continuous characters of S are of the form eins . By Theorem 1.6 , the

set of ...

Page 1037

product clearly converges to zero for 1 = 2x it is readily

T ) is analytic for a # 0 and vanishes only for 2 in o ( T ) . It remains to show that if

a + 0 , then P. ( T ) is continuous in T relative to the Hilbert - Schmidt norm in HS .

product clearly converges to zero for 1 = 2x it is readily

**seen**that the function Pi (T ) is analytic for a # 0 and vanishes only for 2 in o ( T ) . It remains to show that if

a + 0 , then P. ( T ) is continuous in T relative to the Hilbert - Schmidt norm in HS .

Page 1154

Since it is clear that Σ ( 2 ) Ex £ , what will be proved then , is that ( i ) 2 ( 2 ) ( E ) =

c ( 2x2 ) ( E ) , Εε Σ ( 2 ) , for some constant c independent of E. This condition ( i )

, as is

Since it is clear that Σ ( 2 ) Ex £ , what will be proved then , is that ( i ) 2 ( 2 ) ( E ) =

c ( 2x2 ) ( E ) , Εε Σ ( 2 ) , for some constant c independent of E. This condition ( i )

, as is

**seen**from Corollary III.11.6 , is a consequence of the assertion that 2 ( 2 ) ...### What people are saying - Write a review

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

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