Hyperreflexivity of the bounded $n$-cocycle spaces of Banach algebras with matrix representations
作者: Jafar Soltani Farsani
作者单位: 1University of Saskatchewan 106 Wiggins Road S7N 5E6, Saskatoon, Canada
刊名: Studia Mathematica, 2020, Vol.250 , pp.35-55
来源数据库: Institute of Mathematics Polish Academy of Sciences
DOI: 10.4064/sm180611-5-11
原始语种摘要: We study the hyperreflexivity of the bounded $n$-cocycle spaces of Banach algebras with matrix representations. We show how representing elements of a Banach algebra as matrices helps us to prove that the Banach algebra has the strong property $(\mathbb {B})$ with a constant. Consequently, we can prove that if some conditions on the Hochschild cohomology groups are satisfied, then the spaces of bounded $n$-cocycles related to this type of Banach algebras are hyperreflexive and we can provide a bound for their hyperreflexivity constant. This approach in particular can be applied to matrix spaces of arbitrary Banach algebras, finite nest algebras on arbitrary Hilbert spaces and finite CSL algebras on separable Hilbert spaces.
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  • cocycle 上闭键
  • matrix 石基
  • algebra 代数学
  • bounded 有界的
  • cohomology 上同调
  • arbitrary 任意的
  • constant 常数
  • representing 表示
  • prove 实验
  • particular 细致的