Journal of Operator Theory

Volume 72, Issue 2, Fall 2014  pp. 313-329.

$(m,q)$-Isometries on metric spaces

Authors:  Teresa Bermudez (1), Antonio Martinon (2), and Vladimir Muller (3)
Author institution: (1) Departamento de Analisis Matematico, Universidad de La Laguna, 38271 La Laguna (Tenerife), Spain
(2) Departamento de Analisis Matematico, Universidad de La Laguna, 38271 La Laguna (Tenerife), Spain
(3) Mathematical Institute, Czech Academy of Sciences, 115 67 Prague, Czech Republic

Summary:  We show that there exist a linear $m$-isometry on a Hilbert space which is not continuous, and a continuous $m$-isometry on a Hilbert space which is not affine. Further we define $(m,q)$-isometries on metric spaces and prove their basic properties.

DOI: http://dx.doi.org/10.7900/jot.2013jan29.1996
Keywords:  $m$-isometry, metric space, Mazur-Ulam theorem