Weak-polynomial convergence on a Banach space
Weak-polynomial convergence on a Banach space
We show that any super-reflexive Banach space is a <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper Lamda"> <mml:semantics> <mml:mi mathvariant="normal">Λ<!-- Λ --></mml:mi> <mml:annotation encoding="application/x-tex">\Lambda</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-space (i.e., the weak-polynomial convergence for sequences implies the norm convergence). We introduce the notion of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="kappa"> <mml:semantics> <mml:mi>κ<!-- κ --></mml:mi> …