Star order on operator and function algebras

• Autores: M. Bohata
• Localización: Publicationes Mathematicae Debrecen, ISSN 0033-3883, Tomus 79, Fasc. 1-2, 2011, págs. 211-230
• Idioma: inglés
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• Resumen

  • The paper deals with the star order on proper *-algebras. Many results on the star order on matrix algebras and algebras of bounded operators acting on a Hilbert space are generalized to the C*-algebraic context. We characterize the star order on partial isometries in proper *-algebras in terms of their initial and final projections.

    As a corollary, we present a new characterization of infinite C*-algebras. Further, main results concern the infimum and supremum problem for the star order on a C*- algebra C(X) of all continuous complex-valued functions on a Hausdorff topological space X. We show that if X is locally connected or hyperstonean, then any upper bounded set in C(X) has an infimum and a supremum in the star order.