On the ideals of a C*-algebra generated by a family of partial isometries and multipliers

Abstract

© 2015, Pleiades Publishing, Ltd. The C*-subalgebra of the algebra of all bounded operators on the Hilbert space l2 generated by the multiplier algebra and a family of partial isometries satisfying certain relations is considered. The ideals of the algebra under examination and of its quotient by the algebra of compact operators are studied. It is shown that the quotient algebra can be represented as a direct sum of two principal ideals and has nontrivial center.