In an earlier memoir, “Charting
the operator terrain,” a new generalized spectrum for a bounded operator T on a
separable Hilbert space, was defined as follows: Let C∗(T) denote the C∗-algebra
generated by T and the identity operator. We say another operator S is weakly
contained in T if there exists a ∗-representation φ of C∗(T) which maps the identity
into an identity operator and φ(T) = S. The “spectrum” of T, denoted T, is defined
to be the space of unitary equivalence classes of irreducible operators weakly
contained in T. In this paper this spectrum is explicitly computed for certain specific
Toeplitz operators.
