SOME REMARKS ON CESARO-ORLICZ SEQUENCE SPACES

作者：Foralewski Pawel^*; Hudzik Henryk; Szymaszkiewicz Alicja

来源：Mathematical Inequalities & Applications, 2010, 13(2): 363-386.

DOI：10.7153/mia-13-29

• Orlicz function
• Orlicz space
• Cesaro-Orlicz space
• condition delta two
• coordinatewise Kadec-Klee property
• rotundity
• local uniform rotundity
• uniform rotundity

In this paper Cesaro-Orlicz spaces, theory of which started in the papers [7], [28] and [10], are investigated. The problem of the necessity of condition delta(2) for some fundamental topological and geometrical properties is considered again. Criteria for the Kadec-Klee property with respect to the coordinatewise convergence as well as for local uniform convexity of the spaces are given. In the last part, finite dimensional subspaces of Cesaro-Orlicz spaces are investigated.

• 出版日期2010-4