Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Operators with $C^{\ast }$-algebra generated by a unilateral shift


Authors: John B. Conway and Paul McGuire
Journal: Trans. Amer. Math. Soc. 284 (1984), 153-161
MSC: Primary 47B20; Secondary 47C15
DOI: https://doi.org/10.1090/S0002-9947-1984-0742417-7
MathSciNet review: 742417
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: If $T$ is an operator on a Hilbert space $\mathcal {H}$, this paper gives necessary and sufficient conditions on $T$ such that ${C^{\ast } }(T)$, the ${C^{\ast } }$-algebra generated by $T$, is generated by a unilateral shift of some multiplicity. This result is then specialized to the cases in which $T$ is a hyponormal or subnormal operator. In particular, it is shown how to prove a recent conjecture of C. R. Putnam as a consequence of our result.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 47B20, 47C15

Retrieve articles in all journals with MSC: 47B20, 47C15


Additional Information

Keywords: Hyponormal operator, <!– MATH ${C^{\ast } }$ –> <IMG WIDTH="31" HEIGHT="19" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${C^{\ast } }$">-algebra, unilateral shift, subnormal operators
Article copyright: © Copyright 1984 American Mathematical Society