THE RANK FUNCTION OF ANY SIMPLE ALGEBRA

Unitaries in a Simple C-algebra of Tracial Rank One

Let A be a unital separable simple infinite dimensional C∗-algebra with tracial rank no more than one and with the tracial state space T (A) and let U(A) be the unitary group of A. Suppose that u ∈ U0(A), the connected component of U(A) containing the identity. We show that, for any ǫ > 0, there exists a selfadjoint element h ∈ As.a such that ‖u− exp(ih)‖ < ǫ. We also study the problem when u c...

THE DUALITY OF THE L?-REPRESENTATION ALGEBRA ?(S ) OF A FOUNDATION SEMIGROUP S AND FUNCTION ALGEBRAS

In the present paper for a large family of topological semigroups, namely foundation semigroups, for which topological groups and discrete semigroups are elementary examples, it is shown that ?(S) is the dual of a function algebra.

The Dirac Algebra for Any Spin∗

Simple Linearizations of the Simple Pendulum for Any Amplitude∗

Two simple, interpolatory-like linearizations are shown for the simple pendulum which can be used for any initial amplitude.

Completing any low-rank matrix, provably

Matrix completion concerns the recovery of a low-rank matrix from a subset of its revealedentries, and nuclear norm minimization has emerged as an effective surrogate for this combina-torial problem. Here, we show that nuclear norm minimization can recover an arbitrary n × nmatrix of rank r from O(nr log(n)) revealed entries, provided that revealed entries are drawnproportio...