Marco Baronti

The retraction constant in some Banach spaces

Abstract We give new sharper estimations for the retraction constant in some Banach spaces.

Characterizations of inner product spaces by orthogonal vectors

Let X be a real normed space with unit closed ball B. We prove that X is an inner product space if and only if it is true that whenever x, y are points in ?B such that the line through x and y supports 22B then x?y in the sense of Birkhoff.

Diametrically contractive maps and fixed points

Contractive maps have nice properties concerning fixed points; a big amount of literature has been devoted to fixed points of nonexpansive maps. The class of shrinking (or strictly contractive) maps is slightly less popular: few specific results on them (not applicable to all nonexpansive maps) appear in the literature and some interesting problems remain open. As an attempt to fill this gap, a condition half way between shrinking and contractive maps has been studied recently. Here we continue the study of the latter notion, solving some open problems concerning these maps.

Antipodal pairs and the geometry of Banach spaces

In this paper we define and study, in Banach spaces, a new function. We indicate a few relations with some geometric properties of the space (such as uniform convexity) and we calculate the expression of that function in some classical spaces.

An example of asymmetry of convolution operators

Esistono un gruppo compatto non commutativoG∼ ed un operatore di convoluzioneT tale che: perp∈[2,4] e perq∈[1,2),T∈Lpp(G∼) eT∋Lqq(G∼).