‎Given a compact space $X$ and a commutative Banach algebra‎ ‎$A$‎, ‎the character spaces of $A$-valued function algebras on $X$ are‎ ‎investigated‎. ‎The class of natural $A$-valued function algebras‎, ‎those whose characters can be described by means of characters of $A$ and‎ ‎point evaluation homomorphisms‎, ‎is introduced and studied‎. ‎For an‎ ‎admissible Banach $A$-valued function algebra...

Let X, Y be complete metric spaces and E, F be Banach spaces. A bijective linear operator from a space of E-valued functions on X to a space of F -valued functions on Y is said to be biseparating if f and g are disjoint if and only if Tf and Tg are disjoint. We introduce the class of generalized Lipschitz spaces, which includes as special cases the classes of Lipschitz, little Lipschitz and uni...

Let Kn be the Lorentz/second-order cone in IR. For any function f from IR to IR, one can define a corresponding vector-valued function f soc (x) on IR by applying f to the spectral values of the spectral decomposition of x ∈ IR with respect to Kn. It was shown by J.-S. Chen, X. Chen and P. Tseng that this vector-valued function inherits from f the properties of continuity, Lipschitz continuity,...

A class of extended vector fields, called extended divergence-measure fields, is analyzed. These fields include vector fields in Lp and vector-valued Radon measures, whose divergences are Radon measures. Such extended vector fields arise naturally in the study of the behavior of entropy solutions to the Euler equations for gas dynamics and other nonlinear systems of conservation laws. A new not...