Abstract
Every bounded domain in a complex Banach spaceE is biholomorphically equivalent to a finite product of irreducibles if and only ifE does not containc 0. A quantitative version of this holds if and only ifE has finite cotype.
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Dineen, S., Timoney, R.M. Irreducible domains in Banach spaces. Israel J. Math. 57, 327–346 (1987). https://doi.org/10.1007/BF02766218
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DOI: https://doi.org/10.1007/BF02766218