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3 results

  • ESSENTIAL AMENABILITY OF DUAL BANACH ALGEBRAS

  • Part of
  • MOHSEN ZIAMANESH, BEHROUZ SHOJAEE, AMIN MAHMOODI
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 100 / Issue 3 / December 2019
    Published online by Cambridge University Press:
    24 May 2019, pp. 479-488
    Print publication:
    December 2019
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  • We show that an essentially amenable Banach algebra need not have an approximate identity. This answers a question posed by Ghahramani and Loy [‘Generalized notions of amenability’, J. Funct. Anal.  208 (2004), 229–260]. Essentially Connes-amenable dual Banach algebras are introduced and studied.

  • ESSENTIAL CHARACTER AMENABILITY OF BANACH ALGEBRAS

  • Part of
  • RASOUL NASR-ISFAHANI, MEHDI NEMATI
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 84 / Issue 3 / December 2011
    Published online by Cambridge University Press:
    01 November 2011, pp. 372-386
    Print publication:
    December 2011
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  • For a Banach algebra 𝒜 and a character ϕ on 𝒜, we introduce and study the notion of essential ϕ-amenability of 𝒜. We give some examples to show that the class of essentially ϕ-amenable Banach algebras is larger than that of ϕ-amenable Banach algebras introduced by Kaniuth et al. [‘On ϕ-amenability of Banach algebras’, Math. Proc. Cambridge Philos. Soc.144 (2008), 85–96]. Finally, we characterize the essential ϕ-amenability of various Banach algebras related to locally compact groups.

  • ESSENTIAL AMENABILITY OF ABSTRACT SEGAL ALGEBRAS

  • Part of
  • H. SAMEA
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 79 / Issue 2 / April 2009
    Published online by Cambridge University Press:
    13 March 2009, pp. 319-325
    Print publication:
    April 2009
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  • A number of well-known results of Ghahramani and Loy on the essential amenability of Banach algebras are generalized. It is proved that a symmetric abstract Segal algebra with respect to an amenable Banach algebra is essentially amenable. Applications to locally compact groups are given.