Displaying similar documents to “Type and cotype of some Banach spaces.”

Extremely non-complex Banach spaces

Miguel Martín, Javier Merí (2011)

Open Mathematics


A Banach space X is said to be an extremely non-complex space if the norm equality ∥Id +T 2∥ = 1+∥T 2∥ holds for every bounded linear operator T on X. We show that every extremely non-complex Banach space has positive numerical index, it does not have an unconditional basis and that the infimum of diameters of the slices of its unit ball is positive.