Automatic continuity of biseparating maps
We prove that a biseparating map between spaces of vector-valued continuous functions is usually automatically continuous. However, we also discuss special cases when this is not true.
Automatic continuity of linear maps on spaces of continuous functions.
Automorphisms of C commuting with partial integration operators in a rectangle
Convolutional representations of the commutant of the partial integration operators in the space of continuous functions in a rectangle are found. Necessary and sufficient conditions are obtained for two types of representing functions, to be the operators in the commutant continuous automorphisms. It is shown that these conditions are equivalent to the requirement that the considered representing functions be joint cyclic elements of the partial integration operators.
Automorphisms of the algebra of operators in preserving conditioning
Let α be an isometric automorphism of the algebra of bounded linear operators in (p ≥ 1). Then α transforms conditional expectations into conditional expectations if and only if α is induced by a measure preserving isomorphism of [0, 1].
Automorphisms on the spaces of entire functions of several variables over non-archimedean fields.