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I have been working in algebra and ring theory, in particular with rings of operators, involutive rings, Baer *-rings and Leavitt path algebras. These rings were introduced in order to simplify the study of sometimes rather cumbersome operator theory concepts. For example, a Baer *- ring is an algebraic analogue of an AW*-algebra and a Leavitt path algebra is an algebraic analogue of a graph C*-algebra. Such rings of operators can be studied without involving

methods of operator theory. Thus Algebraization of Operator Theory is a common thread between most of the topics of my interest. After some overview of the main ideas of such algebraization, I will focus on one common aspect of some of the rings of operators – the existence of a trace as a way to measure the size of subspaces/subalgebras.

In particular, we adapt some desirable properties of a complex-valued trace on a C*-algebra

to a larger class of algebras.

My website

http://liavas.net

has preprints of my papers and slides from some of my previous presentations as well as a more detailed biography.