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Closed ideals in algebras of smooth functions

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Hanin L. G.

Instytut Matematyczny Polskiej Akademii Nauk

CONTENTS Introduction........................................................................................5 1. Main definitions and basic examples..............................................7 2. Closed ideals in Sobolev algebras...............................................10 2.0. Notation...................................................................................10 2.1. Preliminary observations and results.......................................11 2.2. Closed primary ideals..............................................................13 2.3. Spectral synthesis of ideals.....................................................15 3. Spectral synthesis of ideals in the algebras $C^m Lip φ$............18 4. D-algebras...................................................................................21 5. Zygmund algebras.......................................................................26 5.1. Basic properties.......................................................................26 5.2. Extensions, approximations, and traces...................................32 5.3. Closed primary ideals...............................................................40 5.4. Point derivations......................................................................43 5.5. An extension property and spectral synthesis..........................46 5.6. Proof of Theorem 5.1...............................................................48 Appendix..........................................................................................52 1. Traces of generalized Lipschitz spaces.......................................53 2. Traces of Zygmund spaces.........................................................58 3. Proof of Proposition 5.2.11..........................................................62 References.......................................................................................65

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1 Hanin L. G.

1 1997

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Closed ideals in algebras of smooth functions