## 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 | |

61 other sections not shown

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additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero