We give a solution, via operator spaces, of an old problem in the Morita equivalence of C*-algebras. Namely, we show that C*-algebras are strongly Morita equivalent in the sense of Rieffel if and only if their categories of left operator modules are isomorphic via completely contractive functors. Moreover, any such functor is completely isometrically isomorphic to the Haagerup tensor product (=...

We prove that the the exponential moments of the position operator stay bounded for the supercritical almost Mathieu operator with Diophantine frequency.

In this paper we study the Foias-Williams operator T (Hg) = S∗ Hg 0 S where g ∈ L∞, and Hg is a Hankel operator with symbol g. We exhibit a relationship between the similarity of T (Hg) to a contraction and the rate of decay of {|gn|}n=0, the absolute values of the Fourier coefficients of the symbol g. Let H denote a complex Hilbert space and let L(H) denote the algebra of all bounded linear op...

A theory of singular and quasi-bounded temperatures associated with the heat equation is developed. Guided by the harmonic case [1] an operator S is defined on the set M of non-negative functions on an open set of Rn+l which admit superthermic majorants. Quasi-bounded and singular functions in M are defined from the operator S . The basic properties of S are discussed. Non-negative temperatures...

We show that each power bounded operator with spectral radius equal to one on a reflexive Banach space has a nonzero vector which is not supercyclic. Equivalently, the operator has a nontrivial closed invariant homogeneous subset. Moreover, the operator has a nontrivial closed invariant cone if 1 belongs to its spectrum. This generalizes the corresponding results for Hilbert space operators. Fo...