## Linear Operators: Spectral theory |

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Page 884

The study of ideal theory in B - algebra was inaugurated by Gelfand [ 1 ] to whom

most of the results

of Section 2 are due to Gelfand [ 1 ] . The fundamental Theorem 3.7 was proved ...

The study of ideal theory in B - algebra was inaugurated by Gelfand [ 1 ] to whom

most of the results

**given**in Section 1 are due . B- and B * -algebras . The resultsof Section 2 are due to Gelfand [ 1 ] . The fundamental Theorem 3.7 was proved ...

Page 909

The proof follows immediately , for since L SM , we have ( Lx , x ) = ( Mx , x ) for

every æ in H. Hence the characterization of ini Men

that an SMen for all n - 1 , 2 , .... 5. Spectral Representation Let M be a finite

positive ...

The proof follows immediately , for since L SM , we have ( Lx , x ) = ( Mx , x ) for

every æ in H. Hence the characterization of ini Men

**given**in Theorem 3 showsthat an SMen for all n - 1 , 2 , .... 5. Spectral Representation Let M be a finite

positive ...

Page 1591

The defining property used by them coincides with the property we have

Theorem 4. The development followed in this section and the next , which makes

extensive use of Definition 1 , has also been used by Šnol [ 1 ] and Naïmark [ 5 ] ...

The defining property used by them coincides with the property we have

**given**inTheorem 4. The development followed in this section and the next , which makes

extensive use of Definition 1 , has also been used by Šnol [ 1 ] and Naïmark [ 5 ] ...

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Copyright | |

57 other sections not shown

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