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Compact-Like Operators in Lattice-Normed Spaces | | A. Aydın
; E. Yu. Emelyanov
; N. Erkurşun Özcan
; M. A. A. Marabeh
; | | Date: |
11 Jan 2017 | | 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. | | Source: | arXiv, 1701.3073 | | Services: | Forum | Review | PDF | Favorites | |
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