## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 85

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 ...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

34 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

additive Akad algebra Amer analytic applied assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete 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 measure multiplicity 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