 

John Froelich and Ben Mathes
BiStrictly Cyclic Operators


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


Abstract
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 bistrictly cyclic operator
which leads to theorems about general bistrictly 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 bistrictly cyclic.


Author information
John Froelich:
Department of Mathematics, University of Houston, University Park, Houston, Texas 77204
JohnF12748@aol.com
Ben Mathes:
Department of Mathematics & Computer Science, Colby College, Waterville, ME 04901
dbmathes@colby.edu

