Concerning a geometrical characterization of Fréchet differentiability
We construct a non-m-convex non-commutative -algebra on which all entire functions operate. Our example is also a Q-algebra and a radical algebra. It follows that some results true in the commutative case fail in general.
Every separable nonreflexive Banach space admits an equivalent norm such that the set of the weak-extreme points of the unit ball is discrete.
We study a conditional Fourier-Feynman transform (CFFT) of functionals on an abstract Wiener space . An infinite dimensional conditioning function is used to define the CFFT. To do this, we first present a short survey of the conditional Wiener integral concerning the topic of this paper. We then establish evaluation formulas for the conditional Wiener integral on the abstract Wiener space . Using the evaluation formula, we next provide explicit formulas for CFFTs of functionals in the Kallianpur...
We show that in a super-reflexive Banach space, the conditionality constants of a quasi-greedy basis ℬ grow at most like for some 0 < ε < 1. This extends results by the third-named author and Wojtaszczyk (2014), where this property was shown for quasi-greedy bases in for 1 < p < ∞. We also give an example of a quasi-greedy basis ℬ in a reflexive Banach space with .