## Linear Operators, Part 2 |

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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 .

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 .

Page 909

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

every x in H . Hence the characterization of an , llon

that in Slon for all n = 1 , 2 , . . . . 5 . Spectral Representation Let u be a finite

positive ...

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

every x in H . Hence the characterization of an , llon

**given**in Theorem 3 showsthat in Slon for all n = 1 , 2 , . . . . 5 . Spectral Representation Let u be a finite

positive ...

Page 1273

The simplification ,

presented in the text . ... Krein [ 9 ] has made a systematic study of all the

extensions of a semi - bounded operator , and also

differential ...

The simplification ,

**given**by Freudenthal [ 3 ] , of Friedrichs ' proof is the onepresented in the text . ... Krein [ 9 ] has made a systematic study of all the

extensions of a semi - bounded operator , and also

**given**applications todifferential ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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