Abstract
Two subsets X and Y of a unital C -algebra A are said to be -similar via
s 2 A1 if Y = s1Xs and Y = s1X s. We show that this relation imposes a certain
structure on the sets X and Y, and that under certain natural conditions (for example, if
X is bounded), -similar sets must be unitarily equivalent. As a consequence of our main
results, we present a generalized version of a well-known theorem of W. Specht.