A note on subsymmetric renormings of Banach spaces

Abstract

We revisit the concept of a subsymmetric norm and construct a subsymmetric renorming of a Banach space with a subsymmetric basis. As a by-product of our work we introduce the concept of a lower symmetric basis and investigate its connection with subsymmetric bases and subsymmetric renormings.

Mathematics Subject Classification (2010): Primary 46B15; Secondary 46B03, 46B45.

Keywords: Symmetric bases, subsymmetric bases, renorming, sequence spaces