If $ X $ is an infinite-dimensional uniform algebra, if $ X $ has the Daugavet property or if $ X
$ is a proper $ M $-embedded space, every relatively weakly open subset of the unit ball of …

We study the relation between octahedral norms, Daugavet property and the size of convex
combinations of slices in Banach spaces. We prove that the norm of an arbitrary Banach …

Let E and B be arbitrary weakly compact JB⁎-triples whose unit spheres are denoted by S
(E) and S (B), respectively. We prove that every surjective isometry f: S (E)→ S (B) admits an …

We introduce the notion of Banach Jordan triple modules and determine the precise
conditions under which every derivation from a JB⁎-triple E into a Banach (Jordan) triple E …

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 …

We introduce a natural notion of determinants in matrix JB∗-algebras, ie for hermitian
matrices of biquaternions and for hermitian 3× 3 matrices of complex octonions. We …

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 …

In this work, we study non-rough norms in L (X, Y), the space of bounded linear operators
between Banach spaces X and Y. We prove that L (X, Y) has non-rough norm if and only if …

We prove that every surjective isometry from the unit sphere of the space $ K (H), $ of all
compact operators on an arbitrary complex Hilbert space $ H $, onto the unit sphere of an …

We prove that every biorthogonality preserving linear surjection from a weakly compact JB
$^* $ triple containing no infinite dimensional rank-one summands onto another JB …