Module ( ϕ , ψ ) -amenability of Banach algebras

Abasalt Bodaghi

Archivum Mathematicum (2010)

  • Volume: 046, Issue: 4, page 227-235
  • ISSN: 0044-8753

Abstract

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Let S be an inverse semigroup with the set of idempotents E and S / ≈ be an appropriate group homomorphic image of S . In this paper we find a one-to-one correspondence between two cohomology groups of the group algebra ℓ 1 ( S ) and the semigroup algebra ℓ 1 ( S / ≈ ) with coefficients in the same space. As a consequence, we prove that S is amenable if and only if S / ≈ is amenable. This could be considered as the same result of Duncan and Namioka [5] with another method which asserts that the inverse semigroup S is amenable if and only if the group homomorphic image S / ∼ is amenable, where ∼ is a congruence relation on S .

How to cite

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Bodaghi, Abasalt. "Module $(\varphi ,\psi )$-amenability of Banach algebras." Archivum Mathematicum 046.4 (2010): 227-235. <http://eudml.org/doc/116488>.

@article{Bodaghi2010,
abstract = {Let $S$ be an inverse semigroup with the set of idempotents $E$ and $S/\approx $ be an appropriate group homomorphic image of $S$. In this paper we find a one-to-one correspondence between two cohomology groups of the group algebra $\ell ^1(S)$ and the semigroup algebra $ \{\ell ^\{1\}\}(S/\approx )$ with coefficients in the same space. As a consequence, we prove that $S$ is amenable if and only if $S/\approx $ is amenable. This could be considered as the same result of Duncan and Namioka [5] with another method which asserts that the inverse semigroup $S$ is amenable if and only if the group homomorphic image $S/\sim $ is amenable, where $\sim $ is a congruence relation on $S$.},
author = {Bodaghi, Abasalt},
journal = {Archivum Mathematicum},
keywords = {Banach modules; module derivation; module amenability; inverse semigroup; Banach module; module derivation; module amenability; inverse semigroup},
language = {eng},
number = {4},
pages = {227-235},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Module $(\varphi ,\psi )$-amenability of Banach algebras},
url = {http://eudml.org/doc/116488},
volume = {046},
year = {2010},
}

TY - JOUR
AU - Bodaghi, Abasalt
TI - Module $(\varphi ,\psi )$-amenability of Banach algebras
JO - Archivum Mathematicum
PY - 2010
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 046
IS - 4
SP - 227
EP - 235
AB - Let $S$ be an inverse semigroup with the set of idempotents $E$ and $S/\approx $ be an appropriate group homomorphic image of $S$. In this paper we find a one-to-one correspondence between two cohomology groups of the group algebra $\ell ^1(S)$ and the semigroup algebra $ {\ell ^{1}}(S/\approx )$ with coefficients in the same space. As a consequence, we prove that $S$ is amenable if and only if $S/\approx $ is amenable. This could be considered as the same result of Duncan and Namioka [5] with another method which asserts that the inverse semigroup $S$ is amenable if and only if the group homomorphic image $S/\sim $ is amenable, where $\sim $ is a congruence relation on $S$.
LA - eng
KW - Banach modules; module derivation; module amenability; inverse semigroup; Banach module; module derivation; module amenability; inverse semigroup
UR - http://eudml.org/doc/116488
ER -

References

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  8. Moslehian, M. S., Motlagh, A. N., Some notes on ( σ , τ ) -amenability of Banach algebras, Stud. Univ. Babeş-Bolyai Math. 53 (3) (2008), 57–68. (2008) Zbl1199.46111MR2487108
  9. Munn, W. D., A class of irreducible matrix representations of an arbitrary inverse semigroup, Proc. Glasgow Math. Assoc. 5 (1961), 41–48. (1961) Zbl0113.02403MR0153762
  10. Paterson, A. L. T., Groupoids, Inverse Semigroups, and Their Operator Algebras, Birkhäuser, Boston, 1999. (1999) Zbl0913.22001MR1724106
  11. Rezavand, R., Amini, M., Sattari, M. H., Bagh, D. Ebrahimi, 10.1007/s00233-008-9075-3, Semigroup Forum 77 (2008), 300–305. (2008) MR2443440DOI10.1007/s00233-008-9075-3
  12. Wilde, C., Argabright, L., 10.1090/S0002-9939-1967-0215064-9, Proc. Amer. Math. Soc. 18 (1967), 226–228. (1967) MR0215064DOI10.1090/S0002-9939-1967-0215064-9

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