# Journal of Operator Theory

Volume 77, Issue 2, Spring 2017 pp. 421-454.

Complex symmetric generators for operator algebras

**Authors**:
Junhao Shen (1) and Sen Zhu (2)

**Author institution:** (1) Department of Mathematics and Statistics,
University of New Hampshire, Durham, NH, 03824, U.S.A.
(2) Department of Mathematics, Jilin University, Changchun, 130012, P.R.
China

**Summary: ** In this paper we explore the complex symmetric
generator problem for operator
algebras, that is, the problem of determining which operator
algebras can be generated by a single complex symmetric operator. For type I
von
Neumann algebras, properly infinite von Neumann algebras and a large
class of finite von Neumann algebras, we give a complete answer. The
complex symmetric generator problem for a large class of
$C^*$-algebras, including UHF algebras, AF algebras, irrational
rotation algebras and reduced free products, is also studied.

**DOI: **http://dx.doi.org/10.7900/jot.2016apr25.2116

**Keywords: ** complex symmetric operator, von Neumann algebra,
$C^*$-algebra, anti-automorphism, generator, single generation

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