for suitable banach spaces $x$ and $y$ with schauder decompositions and‎ ‎a suitable closed subspace $mathcal{m}$ of some compact operator space from $x$ to $y$‎, ‎it is shown that the strong banach-saks-ness of all evaluation‎ ‎operators on ${mathcal m}$ is a sufficient condition for the weak‎ ‎banach-saks property of ${mathcal m}$, where for each $xin x$ and $y^*in‎ ‎y^*$‎, ‎the evaluation op...

Weak factorization systems Weak factorization systems are of paramount importance to homotopical algebra. This connection is best illustrated by the following definition, due to Joyal and Tierney [JT07]. Definition 1. A Quillen model structure on a category M, with a class of maps W called weak equivalences satisfying the 2-of-3 property, consists of two classes of maps C and F so that (C ∩W,F)...

Abstract. We define a stronger property than unique ergodicity with respect to the fixed–point subalgebra firstly investigated in [1]. Such a property is denoted as F–strict weak mixing (F stands for the Markov projection onto the fixed–point operator system). Then we show that the free shifts on the reduced C–algebras of RD–groups, including the free group on infinitely many generators, and am...

The fractional weak discrepancy of a poset P , written wdF (P ), is the least k such that some f : P → R satisfies f(y)− f(x) ≥ 1 for x ≺ y and |f(y)− f(x)| ≤ k for x‖y. We determine the minimal forbidden subposets for the property wdF (P ) ≤ k when k is an integer.

In 1926 M. Lavrentiev [7] proposed an example of a variational problem whose infimum over the Sobolev spaceW, for some values of p ≥ 1, is strictly lower than the infimum overW1,∞. This energy gap is known since then as the Lavrentiev phenomenon. The aim of this paper is to provide a deeper insight into this phenomenon by shedding light on an unnoticed feature. Any energy that presents the Lavr...

For suitable Banach spaces $X$ and $Y$ with Schauder decompositions and‎ ‎a suitable closed subspace $mathcal{M}$ of some compact operator space from $X$ to $Y$‎, ‎it is shown that the strong Banach-Saks-ness of all evaluation‎ ‎operators on ${mathcal M}$ is a sufficient condition for the weak‎ ‎Banach-Saks property of ${mathcal M}$, where for each $xin X$ and $y^*in‎ ‎Y^*$‎, ‎the evaluation op...