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Journal of Operator Theory

Volume 45, Issue 1, Winter 2001  pp. 53-80.

Unbounded $C^*$-seminorms and unbounded $C^*$-spectral algebras

Authors:  Subhash J. Bhatt (1), Atsushi Inoue (2) and Hidekazu Ogi (3)
Author institution: (1) Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar 388120, India
(2) Department of Applied Mathematics, Fukuoka University, Nanakuma, Jonan-ku, Fukuoka 814-0180, Japan
(3) Dept. Functional Materials Engineering, Fukuoka Institute of Technology, Wazirohigashi, Higashi-ku, Fukuoka 811-0295, Japan

Summary:  Several $*$-algebras $\cal A$ carry with them unbounded $C^*$-seminorms in the s ense that they are $C^*$-seminorms defined on $*$-subalgebras. Unbounded operator representations of $\cal A$ are constructed from such unbound ed $C^*$-seminorms and they are investigated. The notions of spectrality and sta bility of unbounded $C^*$-seminorms are defined and studied.

Keywords:  (Hereditary) spectral unbounded $C^*$-seminorms, unbounded $*$-represe ntations, stable unbounded $C^*$-seminorms

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