2011/08/06 by Heinz H. Bauschke, Bauschke, Heinz H., Jonathan M. Borwein +5
Computer Science · Mathematics · #47H05 #47N1 #90C25 #Advanced Banach Space Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Optimization and Variational Analysis #Primary 47A06 #Secondary 47B65
paper · pdf · doi:10.48550/arxiv.1108.1463
openalex publication_date 2011/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we construct maximally monotone operators that are not of Gossez's dense-type (D) in many nonreflexive spaces. Many of these operators also fail to possess the Brønsted-Rockafellar (BR) property. Using these operators, we show that the partial inf-convolution of two BC--functions will not always be a BC--function. This provides a negative answer to a challenging question posed by Stephen Simons. Among other consequences, we deduce that every Banach space which contains an isomorphic copy of the James space J or its dual J^*, or c0 or its dual ℓ1, admits a non type (D) operator.