## Linear Operators: Spectral theory |

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Page 877

Then an

Consequently the spectrum of y as an

as an

Then an

**element**y in Ş) has an inverse in 3: if and only if it has an inverse in §).Consequently the spectrum of y as an

**element**of 9) is the same as its spectrumas an

**element**of 3. Proof. If y-1 exists as an**element**of Q) then, since 3 and 9) ...Page 878

Clearly the requirement that a and g(u) = u be corresponding

determines the *-isomorphism uniquely and we are thus led to the following

definition. 12 DEFINITION. Let a be an

let fe C(a(z)).

Clearly the requirement that a and g(u) = u be corresponding

**elements**determines the *-isomorphism uniquely and we are thus led to the following

definition. 12 DEFINITION. Let a be an

**element**of a commutative B"-algebra andlet fe C(a(z)).

Page 1339

An

equivalence classes of

denoted by L2({u,3). We observe that by Lemma 7, the integrand in the integral ...

An

**element**F of Los(uo) will be said to be a {u}-null function if |F = 0. The set of allequivalence classes of

**elements**of Los(uo) modulo (u,3-null functions will bedenoted by L2({u,3). We observe that by Lemma 7, the integrand in the integral ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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