Author: Mathes, Ben, Colby College, Waterville, ME 04901 (dbmathes@colby.edu).
Strictly cyclic algebras with arbitrary prescribed Gelfand spectrum, pp. 823-828.
ABSTRACTGiven any compact subset C of the plane, G. Kalisch shows that there is an operator whose spectrum consists entirely of point spectrum and equals C. We use Banach algebra techniques and the theory of strictly cyclic algebras to give a new proof of this result. In the process, we construct many new examples of strictly cyclic algebras. In particular, we construct a semisimple commutative strictly cyclic algebra whose Gelfand spectrum is homeomorphic to an arbitrary compact subset of Euclidean space.