Vol. 86, No. 2, 1980

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The computation of the generalized spectrum of certain Toeplitz operators

John A. Ernest

Vol. 86 (1980), No. 2, 463–470

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.

Mathematical Subject Classification 2000
Primary: 47B35
Received: 12 May 1978
Published: 1 February 1980
John A. Ernest