## Linear Operators: Spectral theory |

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Page 868

**Commutative**B - Algebras In case X is a**commutative**B - algebra every ideal I is two - sided and the quotient algebra X / 3 is again a**commutative**algebra .Page 869

Every homomorphism of a

Every homomorphism of a

**commutative**B - algebra into the complex number system is continuous . 4 LEMMA . Let M be the set of maximal ideals in the ...Page 882

Show that with the product u * , the Banach space M is a

Show that with the product u * , the Banach space M is a

**commutative**Banach algebra . 14 If f is in L ( -00 , 0 ) , and if 2 ( E ) = Se f ( s ) ds show that ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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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