Unital Compact Homomorphisms between Extended Analytic Lipschitz Algebras
Let 𝑋 and 𝐾 be compact plane sets with 𝐾⊆𝑋. We define 𝐴(𝑋,𝐾)={𝑓∈𝐶(𝑋)∶𝑓|𝐾∈𝐴(𝐾)}, where 𝐴(𝐾)={𝑔∈𝐶(𝑋)∶𝑔 is analytic on int(𝐾)}. For 𝛼∈(0,1], we define Lip(𝑋,𝐾,𝛼)={𝑓∈𝐶(𝑋)∶𝑝𝛼,𝐾(𝑓)=sup{|𝑓(𝑧)−𝑓(𝑤)|/|𝑧−𝑤|𝛼∶𝑧,𝑤∈𝐾,𝑧≠𝑤}<∞} and Lip𝐴(𝑋,𝐾,𝛼)=𝐴(𝑋,𝐾)∩Lip(𝑋,𝐾,𝛼). It is known that Lip𝐴(𝑋,𝐾,𝛼) is a natural Banach f...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/146758 |