## 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

### Keywords:

big disk; bounded hyper-analytic functions; Gleason parts
Full Text:

### References:

 [1] L. Pontryagin, Continuous groups , Nauka, Moscow, 1954 (in Russian). · Zbl 0058.26003 [2] R. Arens and I. Singer, Generalized analytic functions , Trans. Amer. Math. Soc. 81 (1956), 379-393. · Zbl 0078.10902 [3] T. Gamelin, Uniform algebras , Prentice-Hall Inc., Englewood Cliffs, NJ, 1969. · Zbl 0213.40401 [4] J. Garnett, Bounded analytic functions , Academic Press, New York, 1981. · Zbl 0469.30024 [5] S. Grigorian and T. Tonev, Blaschke inductive limits of uniform algebras , Inter. J. Math. Math. Sci. 27 (2001), 599-620. · Zbl 1014.46022 [6] K. Hoffman, Bounded analytic functions and Gleason parts , Ann. Math. 86 (1967), 74-111. · Zbl 0192.48302 [7] D. Stankov, Polynomial approximation of hyper-analytic functions , Serdika 13 (1987), 188-193. · Zbl 0632.30048 [8] —-, Bounded hyper-analytic functions and Shilov boundary , Comt. Acad. Bulg. Sci. 42 (1989), 13-16. · Zbl 0674.30039 [9] T. Tonev, The algebra of bounded hyper-analytic functions has no corona , Analytic functions , Lect. Notes Math. 798 , Springer Verlag, New York, 1980. · Zbl 0451.30040 [10] —-, Big-planes, boundaries and function algebras , Elsevier, North Holland, 1992. · Zbl 0755.46020
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.