Monotonicity properties in Banach spaces via sublinear operators and corrigendum to “Rotundity properties in Banach spaces via sublinear operators, Nonlinear Analysis 64 (2006) 1171–1188”

Various kinds of monotone points (namely lower and upper strictly monotone, lower and upper locally uniformly monotone points) are studied in the space DE(S)DE(S) generated by a Köthe space EE and a sublinear operator SS defined on a Banach lattice XX and with values in EE. Some results on global monotonicity properties are easily deduced from those results. Interpretations of the result in three different classes of the space DE(S)DE(S) are given. At the end a small corrigendum to our paper “Rotundity properties in Banach spaces via sublinear operators” published in Nonlinear Analysis 64 (2006) 1171–1188 is given.