On A Banach space property of Trubnikov

Abstract

Turbnikov/s property ( U , λ, α, β) is investigated. In particular, it is shown that property ( U , λ, α, α, − 1) with α > 1 is equivalent to α-uniform smoothness. It s also shown that property ( U , 1, α, 1) with α > 1 is equivalent to the space being a Hilbert space. The dual property ( U * , γ α α − 1) is also introduced and it is shown that a Banach space X has ( U * , γ α, α − 1) if and only if X is α-uniformly convex.

Locations

• Bulletin of the Australian Mathematical Society - View - PDF