Renormings and the fixed point property in non-commutative -spaces

✍ Scribed by Carlos A. Hernández-Linares; Maria A. Japón

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 239 KB
• Volume: 74
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2011.01.022

✦ Synopsis

Let M be a finite von Neumann algebra. It is known that L 1 (M) and every non-reflexive subspace of L 1 (M) fail to have the fixed point property for non-expansive mappings (FPP). We prove a new fixed point theorem for this class of mappings in non-commutative L 1 (M) Banach spaces which lets us obtain a sufficient condition such that a closed subspace of L 1 (M) can be renormed to satisfy the FPP. As a consequence, we deduce that the predual of every atomic finite von Neumann algebra can be renormed with the FPP.