Stellenbosch University
Extreme point methods in the study of isometries on
certain noncommutative spaces
Pierre de Jager\(^*\), University of South
Africa
Jurie Conradie, University of Cape
Town
SAMS Subject Classification Number: 11
Characterizations of the extreme points (of the unit balls) of various Banach function spaces have often proved useful in obtaining structural descriptions of isometries on those spaces (see for example, [1] and [2]). In this talk we look at how this technique can be employed in the setting of the noncommutative space \(L^1+L^\infty(\mathcal{A})\), where \(\mathcal{A}\) is a semi-finite von Neumann algebra.
References
[1] N.L. Carothers, S.J. Dilworth and D.A. Trautman, On the geometry of the unit spheres of the Lorentz spaces \(L^{w,1}\), Glasgow Math. J. 34 (1992), 21-25.
[2] R. Grzaślewicz and H.H. Schaefer Surjective isometries of \(L^1\cap L^\infty[0,\infty)\) and \(L^1+L^\infty[0,\infty)\), Indag. Math. (N.S.) 3(2) (1992), 173-178.
