Department of Mathematics

Fereidoun Ghahramani


Graduate Students:

Miad Makareh Shireh

Research Areas:

Functional Analysis, Abstract Harmonic Analysis

Recent Publications:

  1. F. Ghahramani, C. J. Read and G.A. Willis. Closed ideal structure and cohomological properties of certain radical Banach algebras, Proc. London Math. Soc.(to appear), 40 pages.
  2. Y.Choi, and F.Ghahramani, Approximate amenability of Schatten classes, Lipschitz algebras and second duals of Fourier algebras, Quart. J.  Math.(Oxford), to appear.
  3. Y. Choi, F. Ghahrmani, Y. Zhang, Apporoximate and pseudo-amenability of various classes of Banach algebras. J. Functional Anal. 256(2009), 3158-3191.
  4. F. Ghahramani, R. J. Loy andY. Zhang, Generalized notions of amenability, II., J. Functional Anal. 245(2008), no. 7, 1776-1810.
  5. F. Ghahramani and R. Stokke, Approximate and pseudo-amenability of the Fourier algebra, Indiana Univ. Math. J. 56(2007), no. 2, 909-930.
  6. F. Ghahramani and Y. Zhang, Pseudo-amenable and pseudo-contractible Banach algebras, Math Proc. Cambridge, Philos. Soc., 142(2007), no. 1, 111-123.
  7. H. Farhadi and F. Ghahramani, Involutions on the second duals of the group algebras and a multiplier problem, Proc. Edinburgh Math.Soc., (2) 50(2007), no.1, 153-161.
  8. F. Ghahramani and A. T. M. Lau, Approximate weak amenability, derivations and Arens regularity of Segal algebras. Studia. Math. 169(2005) no. 2, 189-205.
  9. F. Ghahramani and G. Zabandan, 2-Weak amenability of the Beuring algebras and amenability of their second duals. Int. J. Pure Appl. Math.16(2004) no.1, 75-86.
  10. F.Ghahramani and R. J. Loy, Generalized notions of amenability, J. Functional Analysis 208(2004) no.1, 229-260.
  11. F. Ghahramani and A. T. M. Lau, Weak amenability of certain classes of Banach algebras without bounded approximate identities. Math. Proc. Cambridge Philos.Soc. 133(2002) no.2, 357-371.
  12. H. G. Dales, F. Ghahramani and A.Ya. Helemskii, The amenability of measure algebras, J. London Math. Soc. (2) 66(2002), no. 1, 213-226.
  13. F. Ghahramani and S. Grabiner, Convergence factors and compactness of weighted convolution algebras, Canad. J. Math. 54(2002) no. 2, 303-323.
  14. F. Ghahramani and J. Laali, Amenability and topological centres of the second duals of Banach algebras, Bull. Astral. Math. Soc. Vol. 65(2002) 191-197.
  15. F. Ghahramani, V. Runde and G. A. Willis, Derivations on group algebras, Proc.  London Math. Soc. (3) 80(2000) no.2, 360-390.

Research Interests:

I do research in Functional Analysis and Abstract Harmonic Analysis. The Functional Analysis part of my research divides into three topics: 1. Study of certain linear operators from Banach algebras into related Banach bimodules. These operators may have an additional algebraic constraint; derivations, homomorphisms, involutions and multipliers are among these. 2. Study of the second duals of Banach algebras, when the second duals are equipped with certain products called Arens products. These products naturally extend the products of the zero level algebras. 3.Study of a notion for Banach algebras known as amenability and generalizations of this notion. The Abstract Harmonic Analysis Part of my research is concerend with studying of the above-mentioned operators on certain Banach algebras related to locally compact groups, such as the group algebras, measure algebras, Beurling algebras, Segal algebras, and Fourier algebras. Starting with my Ph.D. thesis (University of Edinburgh,1975-78), among other things, I characterized all the derivations and homomorphisms of the weighted convolution algebras and proved the existence of an isometric (algebra) isomorphism from the measure algebra M(G) of a locally compact group G, onto B(H); the Banach space of all bounded linear operators onto a Hilbert space H. Since then, until very recently, these results have been utilized by several professional researchers in the area and have had direct impact on several Ph.D. theses written at various universities in different parts of the world. In 1988 I proved that the group of the automorphisms of the Volterra algebra is connected in the operator norm topology. Thus I solved a problem which had been open for 20 years. This result has also had an impact on the work of other professional researchers, as well as Ph.D.  theses. Recently, I have been more involved with problems in classical theory of amenability for Banach algebras. In the year 2000, in collaboration with my then NATO grant partenters, Garth Dales(Leeds) and Alexander Helemskii (Moscow State University), we proved that the measure algebra of a non-discrete locally compact group always admits a non-zero point derivation. Thus we answered an open question which had been open since 1976. A by-product of our work was that the measure algebra of non-discrete locally compact group is not amenable - that answered another question open for quite sometime, although there is a difference of opinion on the origin of this problem between some people who had worked it. With Richard J. Loy (Australian National University) we have introduced several new notions of amenability, have developed general theory for these notions and have examined them on concrete classes of Banach algebras. Recently, Yong Zhang has also joined us in carrying out this programme. The most promising of these notions seems to be the notion of approximate amenability. My other colleagues with whom I collaborate in research on these notions are Garth Dales, Ross Stokke and Yemon Choi.

 

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Department of Mathematics