Displaying similar documents to “On certain diameters of bounded sets.”

Extensions of linear operators from hyperplanes of l ( n )

Marco Baronti, Vito Fragnelli, Grzegorz Lewicki (1995)

Commentationes Mathematicae Universitatis Carolinae


Let Y l ( n ) be a hyperplane and let A ( Y ) be given. Denote 𝒜 = { L ( l ( n ) , Y ) : L Y = A } and λ A = inf { L : L 𝒜 } . In this paper the problem of calculating of the constant λ A is studied. We present a complete characterization of those A ( Y ) for which λ A = A . Next we consider the case λ A > A . Finally some computer examples will be presented.

On the frame of the unit ball of Banach spaces

Ryotaro Tanaka (2014)

Open Mathematics


The notion of the frame of the unit ball of Banach spaces was introduced to construct a new calculation method for the Dunkl-Williams constant. In this paper, we characterize the frame of the unit ball by using k-extreme points and extreme points of the unit ball of two-dimensional subspaces. Furthermore, we show that the frame of the unit ball is always closed, and is connected if the dimension of the space is not less than three. As infinite dimensional examples, the frame of the unit...