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Pseudo-hyperbolic distance and Gleason parts of the algebra of bounded hyper-analytic functions on the big disk. (English) Zbl 1335.46047

The content of this paper is best described by its abstract: “Let \(G\) be the compact group of all characters of the additive group of rational numbers, and let \(H^\infty_G\) be the Banach algebra of so-called hyper-analytic functions on the big disk \(\Delta_G\). We characterise the pseudo-hyperbolic distance of the algebra \(H^\infty_G\) in terms of the pseudo-hyperbolic distance of the algebra \(H^\infty\) and establish relationships between Gleason parts in \(M(H^\infty_G)\) and \(M(H^\infty)\).”

MSC:

46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
43A15 \(L^p\)-spaces and other function spaces on groups, semigroups, etc.
30H05 Spaces of bounded analytic functions of one complex variable
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