TY - JOUR
T1 - Narrow operators on vector-valued sup-normed spaces
AU - Bilik, Dmitriy
AU - Kadets, Vladimir
AU - Shvidkoy, Roman
AU - Sirotkin, Gleb
AU - Werner, Dirk
PY - 2002
Y1 - 2002
N2 - We characterise narrow and strong Daugavet operators on C(K, E)-spaces; these are in a way the largest sensible classes of operators for which the norm equation ∥Id-t-T∥ = 1 + ∥T∥ is valid. For certain separable range spaces E, including all finite-dimensional spaces and all locally uniformly convex spaces, we show that an unconditionally pointwise convergent sum of narrow operators on C(K, E) is narrow. This implies, for instance, the known result that these spaces do not have unconditional FDDs. In a different vein, we construct two narrow operators on C([0, l], l1) whose sum is not narrow.
AB - We characterise narrow and strong Daugavet operators on C(K, E)-spaces; these are in a way the largest sensible classes of operators for which the norm equation ∥Id-t-T∥ = 1 + ∥T∥ is valid. For certain separable range spaces E, including all finite-dimensional spaces and all locally uniformly convex spaces, we show that an unconditionally pointwise convergent sum of narrow operators on C(K, E) is narrow. This implies, for instance, the known result that these spaces do not have unconditional FDDs. In a different vein, we construct two narrow operators on C([0, l], l1) whose sum is not narrow.
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U2 - 10.1215/ijm/1258136201
DO - 10.1215/ijm/1258136201
M3 - Article
AN - SCOPUS:0036628215
SN - 0019-2082
VL - 46
SP - 421
EP - 441
JO - Illinois Journal of Mathematics
JF - Illinois Journal of Mathematics
IS - 2
ER -