## Linear Operators: Spectral theory |

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Page 865

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An

**element**æ in a B - subalgebra of the form Xo = epłe , where eo is an idempotent with 0 #lo e clearly has 001x ) Co ( x ) . The following lemma shows that ...Page 877

Then an

Then an

**element**y in Y has an inverse in X if and only if it has an inverse in y . Consequently the spectrum of y as an**element**of Y is the same as its ...Page 1339

An

An

**element**F of Ly ( { Mij } ) will be said to be a { llij } -null function if | F | 0. The set of all equivalence classes of**elements**of Ly ( { ui ...### 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