New York Journal of Mathematics
Volume 1 (1994-1995) 97-110


John Froelich and Ben Mathes

Bi-Strictly Cyclic Operators

Published: April 10, 1995
Keywords: Strictly cyclic, invariant subspace, column Hilbert space, completely bounded, completely isomorphic.
Subject: Primary 47A15; Secondary 46B28.

The genesis of this paper is the construction of a new operator that, when combined with a theorem of Herrero, settles a question of Herrero. Herrero proved that a strictly cyclic operator on an infinite dimensional Hilbert space is never triangular. He later asks whether the adjoint of a strictly cyclic operator is necessarily triangular. We settle the question by constructing an operator T for which both T and T* are strictly cyclic. We make a detailed study of this bi-strictly cyclic operator which leads to theorems about general bi-strictly cyclic operators. We conclude the paper with a comparison of the operator space structures of the singly generated algebras A(S) and A(T), when S is strictly cyclic and T is bi-strictly cyclic.

Author information

John Froelich:
Department of Mathematics, University of Houston, University Park, Houston, Texas 77204

Ben Mathes:
Department of Mathematics & Computer Science, Colby College, Waterville, ME 04901