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

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

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

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

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

Operator theory and function theory in Drury-Arveson space and its quotients

The Drury-Arveson space $H^2_d$, also known as symmetric Fock space or the $d$-shift space, is a Hilbert function space that has a natural $d$-tuple of operators acting on it, which gives it the structure of a Hilbert module. This survey aims to introduce the Drury-Arveson space, to give a panoramic view of the main operator theoretic and function theoretic aspects of this space, and to describe the universal role that it plays in multivariable operator theory and in Pick interpolation theory.Comment: Final version (to appear in Handbook of Operator Theory); 42 page

Mutuality of Rogers's therapeutic conditions and treatment progress in the first three psychotherapy sessions

Abstract Objective: Research on the effects of Rogers’s therapeutic relationship conditions has typically focused on the unilateral provision of empathy, unconditional positive regard, and congruence from therapist to client. Method: This study looked at both client and therapist mutuality of the Rogerian therapeutic conditions and the association between mutuality and treatment progress in the first three psychotherapy sessions. Clients (N = 62; mean age = 24.32; 77% female, 23% male) and therapists (N = 12; mean age = 34.32; nine female and three male) rated one another using the Barrett-Lennard Relationship Inventory after the first and third session. Results: Both clients and therapists perceived the quality of the relationship as improved over time. Client rating of psychological distress (CORE-OM) was lower after session 3 than at session 1 (es = .85, [95% CIs: .67, 1.03]). Hierarchical multiple regression was used to test the predictive power of mutually high levels of the therapeutic conditions on treatment progress. The association between client rating of therapist-provided conditions and treatment progress at session 3 was higher when both clients and therapists rated each other as providing high levels of the therapeutic conditions (R2 change = .073, p < .03). Conclusions: The findings suggest mutuality of Rogers’s therapeutic conditions is related to treatment progress. Keywords: therapeutic relationship; psychotherapy; mutuality; treatment progres

Loneliness, social support and cardiovascular reactivity to laboratory stress

Self-reported or explicit loneliness and social support have been inconsistently associated with cardiovascular reactivity (CVR) to stress. The present study aimed to adapt an implicit measure of loneliness, and use it alongside the measures of explicit loneliness and social support, to investigate their correlations with CVR to laboratory stress. Twenty-five female volunteers aged between 18 and 39 years completed self-reported measures of loneliness and social support, and an Implicit Association Test (IAT) of loneliness. The systolic blood pressure (SBP), diastolic blood pressure (DBP) and heart rate (HR) reactivity indices were measured in response to psychosocial stress induced in the laboratory. Functional support indices of social support were significantly correlated with CVR reactivity to stress. Interestingly, implicit, but not explicit, loneliness was significantly correlated with DBP reactivity after one of the stressors. No associations were found between structural support and CVR indices. Results are discussed in terms of validity of implicit versus explicit measures and possible factors that affect physiological outcomes