Currently I am working on p-operator space and its application to harmonic analysis on locally compact groups.
p-operator space can be regarded as an Lp-space generalization of classical operator space, which is based on Hilbert spaces.
Fourier algebra A(G) on a locally compact group G has turned out to have close connection with various properties of G itself.
For example, it is well-known that a group G is amenable if and only if A(G) has a bounded approximate identity,
and operator space theory has played an important role in studying other relationships between A(G) and G.
Generalizing this idea, we study Figà-Talamanca-Herz algebra Ap(G) which can be thought of as an Lp-space generalization of A(G)
and thus it is natural to study Ap(G) and related algebras in the frame work of p-operator space.
On p-approximation properties for p-operator spaces (with Guimei An and Zhong-Jin Ruan, Journal of Functional Analysis 259 (2010) 933-974)
Conditions $C_p$, $C'_p$, and $C''_p$ for $p$-operator spaces (arXiv:1209.1864)
Hahn-Banach type extension theorems on p-operator spaces (arXiv: 1303.3513)