MULTIPLICATIVE PERTURBATIONS OF STABLE AND CONVERGENT OPERATORS

Some familiar classes of stable Hilbert-space operators are studied to determine how they overlap and where the unitary similarity classes o f their members lie. Analogous, but less familiar, classes of converge nt operators are examined with the same aim. The classes considered ar e often sets of products MA where M is a given set of diagonal or Herm itian matrices and A is a single matrix. The A's for which MA is a set of stable or convergent operators are sometimes characterized. (C) 19 98 Elsevier Science Inc.