Relationships between K-monotonicity and rotundity properties with\n application

2018/02/26 by Maciej Ciesielski, Ciesielski, Maciej
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces

paper · pdf · doi:10.48550/arxiv.1802.09268

Abstract

In this paper we investigate a relationship between fully k-rotundity\nproperties, uniform K-monotonicity properties, reflexivity and K-order\ncontinuity in a symmetric spaces E. We also answer a crucial question whether\nfully k-rotundity properties might be restricted in definition to E^d the\npositive cone of all nonnegative and decreasing elements of E. We present a\ncomplete characterization of decreasing uniform K-monotonicity and K-order\ncontinuity in E. It is worth mentioning that we also establish several\nauxiliary results describing reflexivity in Lorentz spaces and K-order\ncontinuity in Orlicz spaces. Finally, we show an application of discussed\ngeometric properties to the approximation theory.\n

Related

• Strict K-monotonicity and K-order continuity in symmetric spaces
• Counterexamples in rotundity of norms in Banach spaces
• Characterizations of some rotundity properties in terms of farthest points
• 2-rotund norms for unconditional and symmetric sequence spaces
• Spaces C(K) with an equivalent URED norm