On regularity of inductive limits
This article deals with K- and J-spaces defined by means of polygons. First we establish some reiteration formulae involving the real method, and then we study the behaviour of weakly compact operators. We also show optimality of the weak compactness results.
The paper discusses Problems 8 and 88 posed by Stanisław Mazur in the Scottish Book. It turns out that negative solutions to both problems are immediate consequences of the results of Peller [J. Operator Theory 7 (1982)]. We discuss here some quantitative aspects of Problems 8 and 88 and give answers to open problems discussed in a recent paper of Pełczyński and Sukochev in connection with Problem 88.