Reflexivity of the translation-dilation algebras on L^2(R)

The hyperbolic algebra A_h, studied recently by Katavolos and Power, is the weak star closed operator algebra on L^2(R) generated by H^\infty(R), as multiplication operators, and by the dilation operators V_t, t \geq 0, given by V_t f(x) = e^{t/2} f(e^t x). We show that A_h is a reflexive operator algebra and that the four dimensional manifold Lat A_h (with the natural topology) is the reflexive hull of a natural two dimensional subspace.Comment: 10 pages, no figures To appear in the International Journal of Mathematic

Parabolic oblique derivative problem in generalized Morrey spaces

We study the regularity of the solutions of the oblique derivative problem for linear uniformly parabolic equations with VMO coefficients. We show that if the right-hand side of the parabolic equation belongs to certain generalized Morrey space than the strong solution belongs to the corresponding generalized Sobolev-Morrey space

de Branges-Rovnyak spaces: basics and theory

For $S$ a contractive analytic operator-valued function on the unit disk ${\mathbb D}$, de Branges and Rovnyak associate a Hilbert space of analytic functions ${\mathcal H}(S)$ and related extension space ${\mathcal D(S)}$ consisting of pairs of analytic functions on the unit disk ${\mathbb D}$. This survey describes three equivalent formulations (the original geometric de Branges-Rovnyak definition, the Toeplitz operator characterization, and the characterization as a reproducing kernel Hilbert space) of the de Branges-Rovnyak space ${\mathcal H}(S)$, as well as its role as the underlying Hilbert space for the modeling of completely non-isometric Hilbert-space contraction operators. Also examined is the extension of these ideas to handle the modeling of the more general class of completely nonunitary contraction operators, where the more general two-component de Branges-Rovnyak model space ${\mathcal D}(S)$ and associated overlapping spaces play key roles. Connections with other function theory problems and applications are also discussed. More recent applications to a variety of subsequent applications are given in a companion survey article

Optimal solutions to matrix-valued Nehari problems and related limit theorems

In a 1990 paper Helton and Young showed that under certain conditions the optimal solution of the Nehari problem corresponding to a finite rank Hankel operator with scalar entries can be efficiently approximated by certain functions defined in terms of finite dimensional restrictions of the Hankel operator. In this paper it is shown that these approximants appear as optimal solutions to restricted Nehari problems. The latter problems can be solved using relaxed commutant lifting theory. This observation is used to extent the Helton and Young approximation result to a matrix-valued setting. As in the Helton and Young paper the rate of convergence depends on the choice of the initial space in the approximation scheme.Comment: 22 page

The relationships between internal and external threat and right-wing attitudes: A three-wave longitudinal study

The interplay between threat and right-wing attitudes has received much research attention, but its longitudinal relationship has hardly been investigated. In this study, we investigated the longitudinal relationships between internal and external threat and right-wing attitudes using a cross-lagged design at three different time points in a large nationally representative sample (N = 800). We found evidence for bidirectional relationships. Higher levels of external threat were related to higher levels of Right-Wing Authoritarianism and to both the egalitarianism and dominance dimensions of Social Dominance Orientation at a later point in time. Conversely, higher levels of RWA were also related to increased perception of external threat later in time. Internal threat did not yield significant direct or indirect longitudinal relationships with right-wing attitudes. Theoretical and practical implications of these longitudinal effects are discussed

Community‐Engaged Neighborhood Revitalization and Empowerment: Busy Streets Theory in Action

Busy streets theory predicts that engaging residents in physical revitalization of neighborhoods will facilitate community empowerment through the development of sense of community, social cohesion, collective efficacy, social capital, and behavioral action. Establishing safe environments fosters positive street activity, which reinforces neighborhood social relationships. A community‐engaged approach to crime prevention through environmental design (CE‐CPTED) is one promising approach to creating busy streets because it engages residents in collaborative interactions to promote safer environments. Yet, few researchers have studied how CE‐CPTED may be associated with busy streets. We interviewed 18 residents and stakeholders implementing CE‐CPTED in Flint, Michigan. We studied three neighborhoods with different levels of resident control over CE‐CPTED. Participants described how CE‐CPTED implementation affected their neighborhood. Participants from all three neighborhoods reported that CE‐CPTED was associated with positive street activity, sense of community, and collective efficacy. Participants from neighborhoods with higher resident control of CE‐CPTED reported more social capital and behavioral action than those from neighborhoods with less resident control. Our findings support busy streets theory: Community engagement in neighborhood improvement enhanced community empowerment. CE‐CPTED that combines physical revitalization with resident engagement and control creates a potent synergy for promoting safe and healthy neighborhoods.HighlightsBusy streets theory supported in qualitative study of neighborhoods in a rust belt city.Community engaged neighborhood improvement enhances psychological empowerment.Resident control of neighborhood revitalization results in most empowered outcomes of busy streets.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/154635/1/ajcp12358_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154635/2/ajcp12358.pd

Progress in noncommutative function theory

In this expository paper we describe the study of certain non-self-adjoint operator algebras, the Hardy algebras, and their representation theory. We view these algebras as algebras of (operator valued) functions on their spaces of representations. We will show that these spaces of representations can be parameterized as unit balls of certain $W^{*}$-correspondences and the functions can be viewed as Schur class operator functions on these balls. We will provide evidence to show that the elements in these (non commutative) Hardy algebras behave very much like bounded analytic functions and the study of these algebras should be viewed as noncommutative function theory

Representing Kernels of Perturbations of Toeplitz Operators by Backward Shift-Invariant Subspaces

It is well known the kernel of a Toeplitz operator is nearly invariant under the backward shift S∗. This paper shows that kernels of finite rank perturbations of Toeplitz operators are nearly S∗-invariant with finite defect. This enables us to apply a recent theorem by Chalendar–Gallardo–Partington to represent the kernel in terms of backward shift-invariant subspaces, which we identify in several important cases

Educational change in Scotland: Policy, context and biography

The poor success rate of policy for curriculum change has been widely noted in the educational change literature. Part of the problem lies in the complexity of schools, as policymakers have proven unable to micromanage the multifarious range of factors that impact upon the implementation of policy. This paper draws upon empirical data from a local authority-led initiative to implement Scotland’s new national curriculum. It offers a set of conceptual tools derived from critical realism (particularly the work of Margaret Archer), which offer significant potential in allowing us to develop greater understanding of the complexities of educational change. Archer’s social theory developed as a means of explaining change and continuity in social settings. As schools and other educational institutions are complex social organisations, critical realism offers us epistemological tools for tracking the ebbs and flows of change cycles over time, presenting the means for mapping the multifarious networks and assemblages that form their basis