On some Banach space constants arising in nonlinear fixed point and eigenvalue theory
© Appell et al. 2004
Received: 8 June 2004
Published: 26 December 2004
As is well known, in any infinite-dimensional Banach space one may find fixed point free self-maps of the unit ball, retractions of the unit ball onto its boundary, contractions of the unit sphere, and nonzero maps without positive eigenvalues and normalized eigenvectors. In this paper, we give upper and lower estimates, or even explicit formulas, for the minimal Lipschitz constant and measure of noncompactness of such maps.