Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A characterization of the Pedersen ideal of $ CD0(T,B\sb{0}(H))$ and a counter-example


Authors: R. M. Gillette and D. C. Taylor
Journal: Proc. Amer. Math. Soc. 68 (1978), 59-63
MSC: Primary 46L05
DOI: https://doi.org/10.1090/S0002-9939-1978-0461156-6
MathSciNet review: 0461156
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let T be a locally compact Hausdorff space, H a complex Hilbert space, and A the $ {C^\ast}$-algebra $ {C_0}(T,{B_0}(H))$. Let $ {A_0}$ be the Pedersen ideal of A and $ {J_A}$ the two-sided ideal of A consisting of all x having compact support, for which $ \sup \{ \dim x(t):t \in T\} < \infty $. It is known that $ {A_0} \subseteq {J_A}$, and equality has been conjectured by Pedersen. We give a new characterization of $ {A_0}$ which enables us to show that the conjecture is false.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46L05

Retrieve articles in all journals with MSC: 46L05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0461156-6
Article copyright: © Copyright 1978 American Mathematical Society