This is an announcement for the paper “Compact-Like Operators in Lattice-Normed Spaces” by A. Aydınhttps://arxiv.org/find/math/1/au:+Aydin_A/0/1/0/all/0/1, E. Yu. Emelyanovhttps://arxiv.org/find/math/1/au:+Emelyanov_E/0/1/0/all/0/1, N. Erkurşun Özcanhttps://arxiv.org/find/math/1/au:+Ozcan_N/0/1/0/all/0/1, M. A. A. Marabehhttps://arxiv.org/find/math/1/au:+Marabeh_M/0/1/0/all/0/1.
Abstract: A linear operator $T$ between two lattice-normed spaces is said to be $p$-compact if, for any $p$-bounded net $x_{\alpha}$, the net $Tx_{\alpha}$ has a $p$-convergent subnet. $p$-Compact operators generalize several known classes of operators such as compact, weakly compact, order weakly compact, AM-compact operators, etc. Similar to M-weakly and L-weakly compact operators, we define $p$-M-weakly and $p$-L-weakly compact operators and study some of their properties. We also study $up$-continuous and $up$-compact operators between lattice-normed vector lattices.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1701.03073