Journal of Operator Theory

Volume 59, Issue 2, Spring 2008 pp. 417-430.

A Gelfand-Naimark theorem for some $C^*$-algebras with finite dimensional irreducible representations

Authors: Aldo J. Lazar
Author institution: School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel

Summary: We present a description of the $C^*$-algebras with Hausdorff spectrum whose all irreducible representations are finite-dimensional as algebras of continuous cross-sections of certain Banach bundles, thus generalizing a well-known result of J.M.G. Fell, The structure of algebras of operator fieldS, Acta Math. 106$($1961$)$, 233-280, and J. Tomiyama, M. Takesaki, Applications of fibre bundles to the certain class of $C^*$-algebras, Töhoku Math. J. 13$($1961$)$, 498-522, on homogeneous $C^*$-algebras.

Keywords: Liminal $C^*$-algebra, Banach bundle.

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