If S, T ∈ B(H) have Bishop's property (β), does S + T have Bishop's property (β)? In this paper, a special case of this question is studied. Also given are a necessary and sufficient condition for a 2 × 2 operator matrix to have Bishop's property (β). Finally, the Helton class of an operator which has Bishop's property (β) is studied. 1. Introduction. Let B(H) be the algebra of all bounded line...

The recently published Directory for Catechesis by the Pontifical Council Promoting New Evangelisation is handbook all those who are involved in catechetical ministry, ranging from Bishops and Bishops’ Conferences to pastors, priests lay catechists. This article seeks take a pastoral glance at which offers vision catechesis founded on theology of Evangelii Gaudium, with an openness more kerygma...

We use the mirror coupling of Brownian motion to show that under a $\beta\in (0,1)$-dependent Kato type assumption (which is satisfied suitable $L^q$-assumption on electro-magnetic potential, where $q$ depends $\beta$ and dimension $d$) possibly nonsmooth corresponding magnetic Schr\"odinger semigroup in $\mathbb{R}$ has global $L^{p}$-to-$C^{0,\beta}$ H\"older smoothing property for all $p\in ...

For animals that live in a reasonably variable environment the capacity for learning and memory allow them to adapt to the changes they experience. Ecological factors that vary between habitats can affect a range of learning behaviours. Less attention has been directed at how this variation may affect memory processes, or how different ecological variables might interact when shaping cognition ...