On the intrinsic and the spatial numerical range

For a bounded function $f$ from the unit sphere of a closed subspace $X$ of a Banach space $Y$, we study when the closed convex hull of its spatial numerical range $W(f)$ is equal to its intrinsic numerical range $V(f)$. We show that for every infinite-dimensional Banach space $X$ there is a superspace $Y$ and a bounded linear operator $T:X\longrightarrow Y$ such that $\bar{co} W(T)\neq V(T)$. We also show that, up to renormig, for every non-reflexive Banach space $Y$, one can find a closed subspace $X$ and a bounded linear operator $T\in L(X,Y)$ such that $\bar{co} W(T)\neq V(T)$. Finally, we introduce a sufficient condition for the closed convex hull of the spatial numerical range to be equal to the intrinsic numerical range, which we call the Bishop-Phelps-Bollobas property, and which is weaker than the uniform smoothness and the finite-dimensionality. We characterize strong subdifferentiability and uniform smoothness in terms of this property.Comment: 12 page

Ethical Issues in Journalism: Minimizing Harm when Reporting on Children

Meg Gramza explores the ethical challenges the press faces when reporting on sex trafficking, especially when victims are children. She recommends how journalists can meet their obligation to report truth and do so thoroughly, while minimizing risks of additional harm to the victims. William Wharton explores the ethics involved in photographing children who have been victims of crime and how photojournalists can avoid adding to children’s trauma.https://ecommons.udayton.edu/stander_posters/2413/thumbnail.jp

Identifying and Responding to Mental Health in Schools and the Effects on Student Achievement

With an increasing awareness of mental health issue in students, identification of the effects on student achievement and social life are important to success. Schools are beginning to question their role in identifying and helping students reach their full potential. Furthermore, research shows that stress and test anxiety affect all aspects of schools and it is the school\u27s responsibility to address these issues.https://ecommons.udayton.edu/stander_posters/2167/thumbnail.jp