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1. CMB 2011 (vol 54 pp. 680)

Jiménez-Vargas, A.; Villegas-Vallecillos, Moisés
 $2$-Local Isometries on Spaces of Lipschitz Functions Let $(X,d)$ be a metric space, and let $\mathop{\textrm{Lip}}(X)$ denote the Banach space of all scalar-valued bounded Lipschitz functions $f$ on $X$ endowed with one of the natural norms $\| f\| =\max \{\| f\| _\infty ,L(f)\}$ or $\|f\| =\| f\| _\infty +L(f),$ where $L(f)$ is the Lipschitz constant of $f.$ It is said that the isometry group of $\mathop{\textrm{Lip}}(X)$ is canonical if every surjective linear isometry of $\mathop{\textrm{Lip}}(X)$ is induced by a surjective isometry of $X$. In this paper we prove that if $X$ is bounded separable and the isometry group of $\mathop{\textrm{Lip}}(X)$ is canonical, then every $2$-local isometry of $\mathop{\textrm{Lip}}(X)$ is a surjective linear isometry. Furthermore, we give a complete description of all $2$-local isometries of $\mathop{\textrm{Lip}}(X)$ when $X$ is bounded. Keywords:isometry, local isometry, Lipschitz functionCategories:46B04, 46J10, 46E15

2. CMB 2010 (vol 53 pp. 398)

Botelho, Fernanda; Jamison, James
 Projections in the Convex Hull of Surjective Isometries We characterize those linear projections represented as a convex combination of two surjective isometries on standard Banach spaces of continuous functions with values in a strictly convex Banach space. Keywords:isometry, convex combination of isometries, generalized bi-circular projectionsCategories:47A65, 47B15, 47B37