Surjective isometries on Grassmann spaces

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).

Partial Isometries on Banach Spaces

On Isometries of Euclidean Spaces

Surjective Real-Linear Uniform Isometries Between Complex Function Algebras

In this paper, we first give a description of a surjective unit-preserving real-linear uniform isometry $ T : A longrightarrow B$,  where $ A $ and $ B $ are complex function spaces on compact Hausdorff spaces $ X $ and $ Y $, respectively, whenever ${rm ER}left (A, Xright ) = {rm Ch}left (A, Xright )$ and ${rm ER}left (B, Yright ) = {rm Ch}left (B, Yright )$. Next, we give a description of $ T...

On Characterizations of Isometries on Function Spaces

Let X be a Banach space over C. Let T : X → X be an isometric isomorphism (an onto linear operator on X with |Tx| = |x| for all x ∈ X). When X is a Hilbert space, any perturbations of orthonormal basis of X give an isometric isomorphism on X. But, for non-Hilbertian space, one expects that an isometric isomorphism should be something special, and would like to find a characterization for T on s...