Banach space characterizations of unitaries: A survey Page 1 J. Math. Anal. Appl. 369 (2010)
168–178 Contents lists available at ScienceDirect Journal of Mathematical Analysis and …

The aim of this note is to provide several variants of the diameter two properties for Banach
spaces. We study such properties looking for the abundance of diametral points, which …

We prove that, given a real JB*-triple X, there exists a nonempty relatively weakly open
subset of the closed unit ball of X with diameter less than 2 (if and) only if the Banach space …

We show that every Banach space containing isomorphic copies of c 0 can be equivalently
renormed so that every nonempty relatively weakly open subset of its unit ball has diameter …

We study the unknown differences between the size of slices and relatively weakly open
subsets of the unit ball in Banach spaces. We show that every Banach space containing c 0 …

We obtain sufficient conditions on an M-embedded or L-embedded space so that every
nonempty relatively weakly open subset of its unit ball has norm diameter 2. We prove that …

A Banach space X is said to have the Daugavet property if every rank-one operator T: X⟶ X
satisfies∥ Id+ T∥= 1+∥ T∥. We give geometric characterizations of this property in the …

For an infinite Hausdorff compact set K and for any Banach space X we show that every
nonempty weak open subset relative to the unit ball of the space of X-valued functions that …

A Banach space is said to have the diameter two property if every non-empty relatively
weakly open subset of its unit ball has diameter two. We prove that the projective tensor …

We prove that every JB⁎-triple E (in particular, every C⁎-algebra) satisfying the Daugavet
property also satisfies the stronger polynomial Daugavet property, that is, every weakly …