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The bidual of a Banach algebra associated with a bilinear map

  • Sedigheh BarootkoobEmail author
  • AminAllah Khosravi
  • Hamid Reza Ebrahimi Vishki
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Abstract

We associate a Banach algebra \(\mathbf A _\Phi \) to each bounded bilinear map \(\Phi : \mathrm X\times \mathrm Y\rightarrow \mathrm {Z}\) on Banach spaces, and we find out that this Banach algebra can be useful for many purposes in the theory of Banach algebras. For example, the construction of \(\mathbf A _\Phi \) enables us to provide many simple examples of Banach algebras with different topological centers, which are neither Arens regular nor either left or right strongly Arens irregular. It also gives examples of Banach algebras which are not n-weakly amenable for each natural number n. We also find out that the dual of \(\mathbf A _\Phi \) does not enjoy the factorization property of any level.

Keywords

Bidual Arens product Bilinear map Topological center Weak amenability 

Mathematics Subject Classification

Primary 46H20 Secondary 46H25 

Notes

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Copyright information

© Unione Matematica Italiana 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Basic SciencesUniversity of BojnordBojnordIran
  2. 2.Department of Pure MathematicsFerdowsi University of MashhadMashhadIran
  3. 3.Department of Pure Mathematics, Centre of Excellence in Analysis on Algebraic Structures (CEAAS)Ferdowsi University of MashhadMashhadIran

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