Surjective isometries on spaces of differentiable vector-valued functions

Isometries on Spaces of Vector Valued Lipschitz Functions

This paper gives a characterization of a class of surjective isometries on spaces of Lipschitz functions with values in a finite dimensional complex Hilbert space.

Surjective Isometries on Grassmann Spaces

Let H be a complex Hilbert space, n a given positive integer and let Pn(H) be the set of all projections on H with rank n. Under the condition dimH ≥ 4n, we describe the surjective isometries of Pn(H) with respect to the gap metric (the metric induced by the operator norm).

Automatic Continuity and Weighted Composition Operators between Spaces of Vector-valued Differentiable Functions

Let E and F be Banach spaces. It is proved that if Ω and Ω are open subsets of R and R , respectively, and T is a linear biseparating map between two spaces of differentiable functions A(Ω, E) and A(Ω, F ), then p = q, n = m, and there exist a diffeomorphism h of class C from Ω onto Ω, and a map J : Ω → L(E, F ) of class s−C such that for every y ∈ Ω and every f ∈ A(Ω, E), (Tf)(y) = (Jy)(f(h(y)...

Realcompactness and spaces of vector-valued functions

It is shown that the existence of a biseparating map between a large class of spaces of vector-valued continuous functions A(X,E) and A(Y, F ) implies that some compactifications of X and Y are homeomorphic. In some cases, conditions are given to warrant the existence of a homeomorphism between the realcompactifications of X and Y ; in particular we find remarkable differences with respect to t...

On Spaces of Measurable Vector - Valued Functions 399 Proof