A Banach lattice algebra is a Banach lattice, an associative algebra with a sub-multiplicative norm and the product of positive elements should be positive. In this note we study the Arens regularity and cohomological properties of Banach lattice algebras.

In this paper, we  study the Arens regularity properties of module actions. We investigate some properties of topological centers of module actions ${Z}^ell_{B^{**}}(A^{**})$ and  ${Z}^ell_{A^{**}}(B^{**})$ with some conclusions in group algebras.

Regular structures, flat and non-flat, are perceived as regular in a wide range of viewing angles and under varying illumination. In this papers, we exploit this simple observation and develop an invariant measure of pattern regularity. The measure is the maximum of the regularity values obtained for different directions within the pattern. We demonstrate that the regularity feature introduced ...

We give sharp regularity results for the invariant subbundles of hyperbolic dynamical systems and give open dense sets of codimension one systems where this regularity is not exceeded as well as open dense sets of symplectic, geodesic, and codimension one systems where the analogous regularity results of [PSW] are optimal. We produce open sets of symplectic Anosov diffeomorphisms and flows with...

We derived the Kuhn-Tucker theorem by assuming regularity of the binding constraints. With the possibility of corner solutions, regularity is too stringent. The regularity condition will not necessarily apply throughout the constraint set. Verifying the regularity condition requires knowing the optimal solution, but the first-order conditions will not identify the optimal solution unless the re...

In auction and mechanism design, Myerson’s classical regularity condition is often too weak for a quantitative analysis of performance. For instance, ratios between revenue and welfare, or sales probabilities may vanish at the boundary of Myerson regularity. This paper introduces λ-regularity as a quantitative measure of how regular a distribution is. λ-regularity includes Myerson regularity an...