I am working on p-operator spaces which can be regarded as an Lp-space generalization of classical operator space (which is based on Hilbert spaces).
In particular, I am interested in axiomatic characterization of subspace of B(Lp(¥ì)) and the existence of Hahn-Banach type extension theorems under this setting.
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, Operators and Matrices Vol.8 No.4 (2014) 1079-1093)
Hahn-Banach type extension theorems on p-operator spaces, to appear in Operators and Matrices