We show that every separable $C^$-algebra of real rank zero tensorially absorbs the Jiang–Su algebra contains a dense set generators. It follows that, in classifiable, simple, nuclear $C^$-algebra, generic element is generator.

In this paper we consider C0-group of unitary operators on a Hilbert C*-module E. In particular we show that if A?L(E) be a C*-algebra including K(E) and ?t a C0-group of *-automorphisms on A, such that there is x?E with =1 and ?t (?x,x) = ?x,x t?R, then there is a C0-group ut of unitaries in L(E) such that ?t(a) = ut a ut*.

Given a category C and directed partially ordered set J, certain proJ-C on inverse systems in is constructed such that the ordinary pro-category pro-C most special case of singleton J ? {1}. Further, known pro*-category pro*-C becomes proN-C. Moreover, given pro-reflective pair (C, D), J-shape ShJ(C, D) corresponding functor SJ are which, mentioned cases, become well ones. Among several importa...

Let K and X be compact plane sets such that K X. Let P(K)be the uniform closure of polynomials on K. Let R(K) be the closure of rationalfunctions K with poles o K. Dene P(X;K) and R(X;K) to be the uniformalgebras of functions in C(X) whose restriction to K belongs to P(K) and R(K),respectively. Let CZ(X;K) be the Banach algebra of functions f in C(X) suchthat fjK = 0. In this paper, we show th...

Using a classic example proposed by G I Taylor we reconsider through the use of computer algebra the mathematical analysis of a fundamental pro cess in turbulent ow namely How do large scale eddies evolve into smaller scale ones to the point where they are e ectively absorbed by viscosity The explicit symbolic series solution of this problem even for cleverly chosen spe cial cases requires daun...

It is proved that if A is aregular uniform algebra on a compact Hausdorff space X in which every closed ideal is an M-ideal, then A = C(X).