Delta-semidefinite and delta-convex quadratic forms in Banach spaces

A continuous quadratic form ("quadratic form", in short) on a Banach space $X$ is: (a) delta-semidefinite (i.e., representable as a difference of two nonnegative quadratic forms) if and only if the corresponding symmetric linear operator $T\colon X\to X^*$ factors through a Hilbert space; (b) delta-convex (i.e., representable as a difference of two continuous convex functions) if and only if $T$ is a UMD-operator. It follows, for instance, that each quadratic form on an infinite-dimensional $L_p(\mu)$ space ($1\le p \le\infty$) is: (a) delta-semidefinite iff $p \ge 2$; (b) delta-convex iff $p>1$. Some other related results concerning delta-convexity are proved and some open problems are stated.Comment: 19 page

Educational Leadership Challenges in the 21st Century: Closing the Achievement Gap for At-Risk Students

The purpose of this special issue is twofold: To explore the challenges educational leaders face in addressing the achievement gap for at-risk students; and to seek solutions

Educational Considerations, vol. 38(1) Full Issue

Educational Considerations, vol. 38(1)-Fall 2010-Full issu

Table of contents and editorial information for Vol. 38, no. 1, Fall 2010

Table of contents and editorial information for Vol. 38, no. 1, Fall 2010, special issue Educational Leadership Challenges in the 21st Century: Closing the Achievement Gap for At-Risk Students

The Incidence of At-Risk Students in Indiana: A Longitudinal Study

Elementary and secondary students can be impacted by a number of risk factors, all of which can have a negative influence on their academic success