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Non-commutative holomorphic semicocycles

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 نشر من قبل Guy Katriel
 تاريخ النشر 2017
  مجال البحث
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This paper studies holomorphic semicocycles over semigroups in the unit disk, which take values in an arbitrary unital Banach algebra. We prove that every such semicocycle is a solution to a corresponding evolution problem. We then investigate the linearization problem: which semicocycles are cohomologous to constant semicocycles? In contrast with the case of commutative semicocycles, in the non-commutative case non-linearizable semicocycles are shown to exist. Simple conditions for linearizability are derived and are shown to be sharp.



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