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.

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