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WORTH property, García-Falset coefficient and Opial property of infinite sums

Hardtke J.-D.

Commentationes Mathematicae

2015

Vol 55, No. 1

23--44

We prove some results concerning the WORTH property and the García-Falset coefficient of absolute sums of infinitely many Banach spaces. Also, the Opial property/uniform Opial property of infinite ℓp-sums is studied, and some properties analogous to the Opial property/uniform Opial property are discussed for Lebesgue–Bochner spaces Lpμ; X.

Weak nearly uniform soothness and worth property of [fi]-direct sums of Banach spaces

Kato M., Tamura T.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2006

Vol. 46, [Z] 1

113-129

We shall characterize the weak nearly uniform smoothness of the fi-direct sum X Y of Banach spaces X and Y . The Schur and WORTH properties will be also characterized. As a consequence we shall see in the [...]-sums of Banach spaces there are many examples of Banach spaces with the fixed point property which are not uniformly non-square.