Operator Theory

C* Algebras were first studied in connection with modeling observables in quantum mechanics. They have subsequently generated a lot of interest as an area of research. Fixed point theory is the investigation of existence, uniqueness and approximation of fixed points of mappings. From economics (Nash’s theorem) to physics (phase transitions) there is a wide variety of applications of this exciting area of research. Dr. Shah’s research focuses on these two areas. In the area of C-algebras and Operator Theory, his work has mainly focused on the study of the space - the spectrum of a C-algebra A (consisting of equivalence classes of irreducible *-representations) with hull-kernal topology, and the (related) spaces P(A), G(A) ( A Banach dual of A) - the space of pure states and the space of pure functionals of A, respectively, with the (induced) weak*-topology. He has also published in the area of fixed point theory.