No abstract uploaded!

No abstract uploaded!

No abstract uploaded!

In this paper, we characterize, for 1≤$p$<∞, the multiple ($p$, 1)-summing multilinear operators on the product of$C(K)$spaces in terms of their representing polymeasures. As consequences, we obtain a new characterization of ($p$, 1)-summing linear operators on$C(K)$in terms of their representing measures and a new multilinear characterization of$L$_{∞}spaces. We also solve a problem stated by M.S. Ramanujan and E. Schock, improve a result of H. P. Rosenthal and S. J. Szarek, and give new results about polymeasures.

Let$X$be a smooth$n$-dimensional projective variety embedded in some projective space ℙ^{$N$}over the field ℂ of the complex numbers. Associated with the general projection of$X$to a space ℙ^{$N$-$m$}($N$-$m$>$n$+1) one defines an extended Gauss map $\overline{\gamma}\colon\overline{X}\rightarrow\text{Gr}(n;N-m)$ (in case$N$-$m$>2$n$-1 this is the Gauss map of the image of$X$under the projection). We prove that $\overline{X}$ is smooth. In case any two different points of$X$do have disjoint tangent spaces then we prove that $\overline{\gamma}$ is injective.