Let $\chi^{2}$ denote the space of all double gai sequences. Let $\Lambda^{2}$ denote the space of all double analytic sequences. In this paper we introduce the concept of sectional analyticity. We also prove a theorem on type $M_{\left(\chi^{2}:\chi^{2}\right)}$ and also the mean value condition is established. We construct a mildly conservative FK-space, which is not semi-conservative.