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- W1974568275 abstract "For a complex Banach space X, let A u (B X ) be the Banach algebra of all complex valued functions defined on B X that are uniformly continuous on B X and holomorphic on the interior of B X , and let A wu (B X ) be the Banach subalgebra consisting of those functions in A u (B X ) that are uniformly weakly continuous on B X . In this paper we study a generalization of the notion of boundary for these algebras, originally introduced by Globevnik. In particular, we characterize the boundaries of A wu (B X ) when the dual of X is separable. We exhibit some natural examples of Banach spaces where this characterization provides concrete criteria for the boundary. We also show that every non-reflexive Banach space X which is an M-ideal in its bidual cannot have a minimal closed boundary for A u (B X )." @default.
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- W1974568275 date "2009-01-01" @default.
- W1974568275 modified "2023-10-14" @default.
- W1974568275 title "Boundaries for spaces of holomorphic functions on M-ideals in their biduals" @default.
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- W1974568275 doi "https://doi.org/10.1512/iumj.2009.58.3807" @default.
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