## Linear Operators: Spectral theory |

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Page 868

two-sided and the quotient algebra 3/8 is again a

a B-algebra if Ø is closed (1.13). It is readily seen that every ideal & in 3 which ...

**Commutative**B-Algebras In case 3 is a**commutative**B-algebra every ideal & istwo-sided and the quotient algebra 3/8 is again a

**commutative**algebra. It will bea B-algebra if Ø is closed (1.13). It is readily seen that every ideal & in 3 which ...

Page 869

Every homomorphism of a

system is continuous. 4 LEMMA. Let ~& be the set of marimal ideals in the

Every homomorphism of a

**commutative**B-algebra into the compler numbersystem is continuous. 4 LEMMA. Let ~& be the set of marimal ideals in the

**commutative**B-algebra 3. Then a (~& ) = 0 (ar) and sup ar(N)*) = lim r"||s". SJR e.Page 882

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. where E is

an arbitrary Borel subset of R, and E1 = {(x, y) e Rx R |a-i-ye E}. Show that with

the product u + 2 the Banach space M is a

...

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. where E is

an arbitrary Borel subset of R, and E1 = {(x, y) e Rx R |a-i-ye E}. Show that with

the product u + 2 the Banach space M is a

**commutative**Banach algebra. 14 If f is...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

48 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 adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero