Applications of spreading models to regular methods of summabilities and growth rate of Cesàro means (Q1801836)

The authors present applications of Brunel-Sucheston's spreading model. One application is to show that each weakly null sequence of Banach spaces has a subsequence which is either uniformly completely Cesàro summable or uniformly completely non Cesàro summable. Another application is to show an alternative theorem concerning bounded sequences of Banach spaces with respect to regular methods of summability. A third application is to estimate, from above or below, the growth rate of Cesàro means.