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Opial's modulus in Köthe sequence spaces

Cui Y., Li Y., Płuciennik R.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

1999

[Z] 39

43-56

It is found a modified formula for Opial's modulus rX of order continuous Köthe sequence space X without Schur's property. By using this result, the Opial's modulus of Lebesgue sequence spaces as well as Cesaro sequence spaces can be computed easily. Moreover it is proved in the Köthe se-quence space X with the Fatou property the condition rX(1)>0 implies the order continuity of X.