# Journal of Operator Theory

Volume 49, Issue 2, Spring 2003 pp. 389-405.

Spectral invariance, K-theory isomorphism and an application to the differential structure of $C^*$-algebras**Authors**: S.J. Bhatt, (1) A. Inoue, (2) and H. Ogi (3)

**Author institution:**(1) Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar 388120, India; Current address: Department of Mathematics and Statistics, Case Western Reserve University, Cleveland, Ohio 43403, USA

(2) Department of Applied Mathematics, Fukuoka University, Nanakuma, Jonan-ku Fukuoka 814-0180, Japan

(3) Department of Functional Materials Engineering Fukuoka Institute of Technology, Wazirohigash Higashi-ku Fukuoka 811-0295, Japan

**Summary:**The notion of spectral invariance of a locally convex $*$-algebra is defined by constructing the enveloping $C^*$-algebra and is characterized. It is shown that the spectral invariance induces ${\rm K}$-theory isomorphism at a general level. As an application, the differential structure o f $C^*$-algebras is studied.

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