Amenability and the second dual of a Banach algebra

Frédéric Gourdeau

Studia Mathematica (1997)

  • Volume: 125, Issue: 1, page 75-81
  • ISSN: 0039-3223

Abstract

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Amenability and the Arens product are studied. Using the Arens product, derivations from A are extended to derivations from A**. This is used to show directly that A** amenable implies A amenable.

How to cite

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Gourdeau, Frédéric. "Amenability and the second dual of a Banach algebra." Studia Mathematica 125.1 (1997): 75-81. <http://eudml.org/doc/216423>.

@article{Gourdeau1997,
abstract = {Amenability and the Arens product are studied. Using the Arens product, derivations from A are extended to derivations from A**. This is used to show directly that A** amenable implies A amenable.},
author = {Gourdeau, Frédéric},
journal = {Studia Mathematica},
keywords = {amenability; Arens regularity; second dual; Arens product; derivations},
language = {eng},
number = {1},
pages = {75-81},
title = {Amenability and the second dual of a Banach algebra},
url = {http://eudml.org/doc/216423},
volume = {125},
year = {1997},
}

TY - JOUR
AU - Gourdeau, Frédéric
TI - Amenability and the second dual of a Banach algebra
JO - Studia Mathematica
PY - 1997
VL - 125
IS - 1
SP - 75
EP - 81
AB - Amenability and the Arens product are studied. Using the Arens product, derivations from A are extended to derivations from A**. This is used to show directly that A** amenable implies A amenable.
LA - eng
KW - amenability; Arens regularity; second dual; Arens product; derivations
UR - http://eudml.org/doc/216423
ER -

References

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  1. [1] R. Arens, The adjoint of a bilinear operation, Proc. Amer. Math. Soc. 2 (1951), 839-848. Zbl0044.32601
  2. [2] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, New York, 1973. Zbl0271.46039
  3. [3] I. G. Craw and N. J. Young, Regularity of multiplication in weighted group and semigroup algebras, Quart. J. Math. Oxford Ser. (2) 25 (1974), 351-358. Zbl0304.46027
  4. [4] F. Ghahramani, R. Loy and G. A. Willis, Amenability and weak amenability of second conjugate Banach algebras, Proc. Amer. Math. Soc., to appear. Zbl0851.46035
  5. [5] F. Gourdeau, Amenability of Banach algebras, Ph.D. Thesis, University of Cambridge, 1989. Zbl0717.46042
  6. [6] F. Gourdeau, Amenability of Lipschitz algebras, Math. Proc. Cambridge Philos. Soc. 112 (1992), 581-588. Zbl0782.46043
  7. [7] N. Grønbæk, Amenability of weighted discrete convolution algebras on cancellative semigroups, Proc. Roy. Soc. Edinburgh Sect. A 110 (1988), 351-360. Zbl0678.46038
  8. [8] N. Grønbæk, A characterization of weak amenability, Studia Math. 94 (1989), 149-162. 
  9. [9] B. E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc. 127 (1972). Zbl0256.18014
  10. [10] N. J. Young, The irregularity of multiplication in group algebras, Quart. J. Math. Oxford Ser. (2) 24 (1973), 59-62. Zbl0252.43009

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