Interests

• Abstract harmonic analysis on locally compact quantum groups
• Functional analysis, especially Banach algebras and its interplay with abstract harmonic analysis
• Notions of amenability on Banach algebra and function spaces related to locally compact toplogical groups
• Topological center of second dual of Banach algebras and bilinear maps

Research Projects

• On amenability of actions of Lau algebras

  Approved : 12/10/2012 ~~~ Start : 12/10/2012 ~~~ End : 06/20/2013

  Abstract:

  A notion of an amenable action of a Lau algebra on a von Neumann algebra is introduced. Amenable action of Lau algebras are characterized by a fixed point property. In particular, a fixed point characterization of  H-amenable representation of groups is given.

   

• On certain product of Banach modules

  Abstract:

  Let $A$ and $B$ are Banach algebras such that $B$ is an algebraic Banach $A$-bimodule. We define a product $A\bowtie B$, which is a strongly splitting Banach algebra extension of $A$ by $B$. We obtain characterizations of bounded approximate identities, spectrum, topological center, and study the amenability and weak amenability of these products. This provides a unified approach for obtaining some known results of both module extensions and Lau product of Banach algebras.