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Homogeneous algebras on the circle. II. Multipliers, Ditkin conditions

Colin Bennett, John E. Gilbert (1972)

Annales de l'institut Fourier

This paper considers the Lipschitz subalgebras Λ ( α , p , 𝒜 ) of a homogeneous algebra on the circle. Interpolation space theory is used to derive estimates for the multiplier norm on closed primary ideals in Λ ( α , p ; 𝒜 ) , α [ α ] . From these estimates the Ditkin and Analytic Ditkin conditions for Λ ( α , p ; 𝒜 ) follow easily. Thus the well-known theory of (regular) Banach algebras satisfying the Ditkin condition applies to Λ ( α ; , p ; 𝒜 ) as does the theory developed in part I of this series which requires the Analytic Ditkin condition.Examples are discussed...

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