Pseudodifferential operators with C*-algebra-valued symbols: Abstract characterizations

Given a separable unital C*-algebra C with norm parallel to center dot parallel to, let E-n denote the Banach-space completion of the C-valued Schwartz space on R-n with norm parallel to f parallel to(2)=parallel to < f, f >parallel to(1/2), < f, g >=integral f(x)* g(x)dx. The assignment of the pseudodifferential operator A=a(x,D) with C-valued symbol a(x,xi) to each smooth function with bounded derivatives a is an element of B-C(R-2n) defines an injective mapping O, from B-C(R-2n) to the set H of all operators with smooth orbit under the canonical action of the Heisenberg group on the algebra of all adjointable operators on the Hilbert module E-n. In this paper, we construct a left-inverse S for O and prove that S is injective if C is commutative. This generalizes Cordes' description of H in the scalar case. Combined with previous results of the second author, our main theorem implies that, given a skew-symmetric n x n matrix J and if C is commutative, then any A is an element of H which commutes with every pseudodifferential operator with symbol F(x+J xi), F is an element of B-C(R-n), is a pseudodifferential operator with symbol G(x - J xi), for some G is an element of B-C(R-n). That was conjectured by Rieffel.

Music and faith: The religious scene in the Brazilian phonographic market

This text discusses the phonographic segment of religious music in Brazil in its two main manifestations, linked respectively to the Catholic and Protestant traditions. The text offers a brief history of both traditions, as well as a description of their main recording companies and artists of greatest prominence. In its final part. the text presents the strategies that bring together recording companies and independent artists, as well as ponders over Brazil`s independent musical production as a whole.

Religions and cultures: Religious dynamics in Latin America

The author seeks to analyse the relationships between religion and culture in Latin America, especially in Brazil, highlighting the fact that the different religions enjoy diverse relationships with culture in a single location. He also addresses the fact that religions interpret culture in different ways and these interpretations help define their conversion strategies and how best to confront opposing religions. For the sake of discussion, the author considers, hypothetically, a not-so-distant future in which Latin America becomes predominantly evangelical, and asks what will happen to Latin America`s supposed Catholic culture if the evangelical religions do indeed take over.