Noncommutative spectral synthesis for the involutive Banach algebra associated with a topological dynamical system

Joint and Generalized Spectral Radius of Upper Triangular Matrices with Entries in a Unital Banach Algebra

In this paper, we discuss some properties of joint spectral {radius(jsr)} and  generalized spectral radius(gsr)  for a finite set of upper triangular matrices with entries in a Banach algebra and represent relation between geometric and joint/generalized spectral radius. Some of these are in scalar matrices, but  some are different. For example for a bounded set of scalar matrices,$Sigma$, $r_*...

On Noncommutative Involutive Divisions

Buchberger’s algorithm for computing a Gröbner basis solves the ideal membership problem over commutative polynomial rings. In the early 1990’s, an alternative to this algorithm was found, namely the involutive basis algorithm, which provides a Gröbner basis with extra combinatorial properties. Buchberger’s work was generalised to noncommutative polynomial rings by Bergman and Mora during the 1...

Noncommutative involutive bases

Gröbner Basis theory originated in the work of Buchberger [4] and is now considered to be one of the most important and useful areas of computer algebra. In 1993, Zharkov and Blinkov [13] proposed an alternative method of computing a commutative Gröbner Basis, namely the computation of an Involutive Basis. In the mid 1980’s, Mora showed [11] that Buchberger’s work could be generalised for nonco...

Math 206: Banach Algebra and Spectral Theory

Spectral Synthesis for Banach Algebras , Ii

This paper continues the study of spectral synthesis and the topologies τ ∞ and τ r on the ideal space of a Banach algebra, concentrating particularly on the class of Haagerup tensor products of C *-algebras. For this class, it is shown that spectral synthesis is equivalent to the Hausdorffness of τ ∞. Under a weak extra condition, spectral synthesis is shown to be equivalent to the Hausdorffne...