ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 16, 46, 47 Jain, S. K., Ohio University, U. S. A., Singh, Ajit Iqbal, University of Delhi, India Maximal quotient rings of algebras of functions and operators The maximal quotient ring Q_{max}(R) of the ring R = C(X) of continuous real (or complex) functions on a completely regular Hausdorff space is constructed in terms of continuous functions defined on dense open subsets of X. For certain classes of spaces, including that of metric spaces, Q_{max}(R) turns out to be the classical quotient ring Q_{cl}(R). An example is given to show that this is not true in general. We indicate that the maximal right and left quotient rings of the operator algebra B(H) of a complex (or real) Hilbert space H are anti-isomorphic full linear rings. The notion of maximal topological quotient rings is also introduced.