LIGHT GROUPS OF ISOMORPHISMS OF BANACH SPACES AND INVARIANT LUR RENORMINGS

Author(s)

Antunes, Leandro ^[1] ; Ferenczi, Valentin ^[2] ; Grivaux, Sophie ^[3] ; Rosendal, Christian ^[4]

Affiliation

^[1] Univ Tecnol Fed Parana, Dept Matemat, Campus Toledo, Toledo, PR - Brazil

^[2] Univ Sao Paulo, Inst Matemat & Estat, Dept Matemat, Sao Paulo, SP - Brazil

^[3] Univ Lille, CNRS, UMR 8524, Lab Paul Painleve, Lille - France

^[4] Univ Illinois, Dept Math Stat & Comp Sci, Chicago, IL 60680 - USA

• Document type: Journal article
• Source: PACIFIC JOURNAL OF MATHEMATICS; v. 301, n. 1, p. 31-54, JUL 2019.
• Web of Science Citations: 0

Abstract

Megrelishvili (2001) defines light groups of isomorphisms of a Banach space as the groups on which the weak and strong operator topologies coincide, and proves that every bounded group of isomorphisms of Banach spaces with the point of continuity property (PCP) is light. We investigate this concept for isomorphism groups G of classical Banach spaces X without the PCP, specially isometry groups, and relate it to the existence of G -invariant LUR or strictly convex renormings of X. (AU)

• FAPESP's process: 16/25574-8 - Geometry of Banach Spaces
• Grantee: Valentin Raphael Henri Ferenczi
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 13/11390-4 - Twisted sums, positions and Ramsey theory in Banach Spaces
• Grantee: Valentin Raphael Henri Ferenczi
• Support Opportunities: Regular Research Grants