This is an announcement for the paper “Remarks on bounded operators in $\ell$-Köthe spaces” by Ersin Kizgut, Elif Uyanik and Murat Yurdakul.

Abstract: For locally convex spaces $X$ and $Y$, the continuous linear map $T: X\rightarrow Y$ is said to be bounded if it maps zero neighborhoods of $X$ into bounded sets of $Y$. We denote $(X, Y)\in B$ when every operator between $X$ and $Y$ is bounded. For a Banach space $\ell$ with a monotone norm $|\cdot|$ in which the canonical system $(e_n)$ forms an unconditional basis, we consider $\ell$ -K$"$othe spaces as a generalization of usual K$"$othe spaces. In this note, we characterize $\ell$ -K$"$othe spaces $\ell(a_{pn})$ and $\ell(b_{sm})$ such that $(\ell(a_{pn}),\ell(b_{sm}))\in B$. A pair $(X, Y)$ is said to have the bounded factorization property, and denoted $(X, Y)\in BF$ , if each linear continuous operator $T: X\rightarrow X$ that factors over $Y$ is bounded. We also prove that injective tensor products of some classical K$"$othe spaces have bounded factorization property.

The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1604.05298