2013/04/21 by Alcides Buss, Buss, Alcides, Siegfried Echterhoff +1 · 1 citation
Mathematics · Medicine · #22D35 #46L55 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #Takotsubo Cardiomyopathy and Associated Phenomena
paper · pdf · doi:10.48550/arxiv.1304.5697
openalex publication_date 2013/04/21 · openalex created_date 2022/08/22 · openalex updated_date 2026/07/28
Given a C*-dynamical system (A,G,\α), we say that A is a weakly proper\n(X rtimes G)-algebra if there exists a proper G-space X together with a\nnondegenerate G-equivariant *-homomorphism \φ:C0(X)->M(A). Weakly proper\nG-algebras form a large subclass of the class of proper G-algebras in the sense\nof Rieffel. In this paper we show that weakly proper (X rtimes G)-algebras\nallow the construction of full fixed-point algebras AG corresponding to the\nfull crossed product A rtimes\αG, thus solving, in this setting, a\nproblem stated by Rieffel in his 1988's original article on proper actions. As\nan application we obtain a general Landstad duality result for arbitrary\ncoactions together with a new and functorial construction of maximalizations of\ncoactions.\n The same methods also allow the construction of exotic generalized\nfixed-point algebras associated to crossed-product norms lying between the\nreduced and universal ones. Using these, we give complete answers to some\nquestions on duality theory for exotic crossed products recently raised by\nKaliszewski, Landstad and Quigg.\n