This volume presents the Proceedings of the joint US/Israel Workshop on Operator Theory and its Applications, held in February 1992 at the Ben Gurion University of the Negev. The volume contains a selection of papers covering a wide range of topics in modern operator theory and its applications, from abstract operator theory, to system theory and computers in operator models. The papers treat linear and nonlinear problems, and study operators from different abstract and concrete classes. It is suitable for both pure and applied mathematicians, and engineers.

Our goal is to find Grabner bases for polynomials in four different sets of expressions: 1 x-, (1 - x)-1 (RESOL) X, 1 x- (1 - xy)-1 (EB) X, y-1, (1-yx)-1 y, (1_y)-1 (1-x)-1 (preNF) (EB) plus and (1 - xy)1/2 (1 - yx )1/2 (NF) (preNF) plus and Most formulas in the theory of the Nagy-Foias operator model NF] are polynomials in these expressions where x = T and y = T*. Complicated polynomials can often be simplified by applying "replacement rules." For example, the polynomial (1 - xy)-2 - 2xy(1-xy)-2 + xy2 (1 - xy)-2 -1 simplifies to O. This can be seen by three applications of the replacement...