On the converse of Banach "fixed-point principle"
For some pairs (X,A), where X is a metrizable topological space and A its closed subset, continuous, linear (i.e., additive and positive-homogeneous) operators extending metrics for A to metrics for X are constructed. They are defined by explicit analytic formulas, and also regarded as functors between certain categories. An essential role is played by "squeezed cones" related to the classical cone construction. The main result: if A is a nondegenerate absolute neighborhood retract for metric spaces,...
S. CHEVET, p-ellipsoïdes de . Mesures cylindriques gaussiennes 439-441 W. WOJTYŃSKI On conditional bases in non-nuclear Fréchet spaces 441 C. BESSAGA, A theorem on complemented subspaces of nuclear spaces 441-442 C. MCCARTHY, Optimal conditioning of operators 442-443 D. PRZEWORSKA-ROLEWICZ, On algebraic derivative 443-444 N. TOMCZAK, A remark (p,q)-absolutely summing operators in -spaces 444-445 W. MLAK, Decompositions of operator representations of function algebras 445-446 A. PERSSON, p-integral...
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