## 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 .

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 , Mn

that hn Mn 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 , Mn

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

positive ...

Page 1149

likewise

representations , which , if one tries to regard them as representations of the

rotation group itself , turn out to be doublevalued . These representations are the

so ...

likewise

**given**by irreducible sets of tensors . The group RŮ ( n ) has additionalrepresentations , which , if one tries to regard them as representations of the

rotation group itself , turn out to be doublevalued . These representations are the

so ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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