Correction to the paper: Support functionals and smoothness in Musielak-Orlicz sequence spaces endowed with the Luxemburg norm
Corrigendum to “Commutators on ” (Studia Math. 206 (2011), 175-190)
We give a corrected proof of Theorem 2.10 in our paper “Commutators on ” [Studia Math. 206 (2011), 175-190] for the case 1 < q < p < ∞. The case when 1 = q < p < ∞ remains open. As a consequence, the Main Theorem and Corollary 2.17 in that paper are only valid for 1 < p,q < ∞.
Cotype and (q, 1)-summing norm in a Banach space.
Cotype for p-Banach spaces
Cotype of operators from C(K).
Countably convex sets
We investigate countably convex subsets of Banach spaces. A subset of a linear space is countably convex if it can be represented as a countable union of convex sets. A known sufficient condition for countable convexity of an arbitrary subset of a separable normed space is that it does not contain a semi-clique [9]. A semi-clique in a set S is a subset P ⊆ S so that for every x ∈ P and open neighborhood u of x there exists a finite set X ⊆ P ∩ u such that conv(X) ⊈ S. For closed sets this condition...
Criteria for in Musielak-Orlicz spaces
In this paper, some necessary and sufficient conditions for in Musielak-Orlicz function spaces as well as in Musielak-Orlicz sequence spaces are given.