Weak isometries of Hamming spaces

On Isometries of Euclidean 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 weak isometries of Preparata codes

Let C1 and C2 be codes with code distance d. Codes C1 and C2 are called weakly isometric, if there exists a mapping J : C1 → C2, such that for any x, y from C1 the equality d(x, y) = d holds if and only if d(J(x), J(y)) = d. Obviously two codes are weakly isometric if and only if the minimal distance graphs of these codes are isomorphic. In this paper we prove that Preparata code of length n ≥ ...

Weak C-Hopf Algebras and Multiplicative Isometries

We show how the data of a finite dimensional weak C∗-Hopf algebra can be encoded into a pair (H, V ) where H is a finite dimensional Hilbert space and V :H⊗H → H⊗H is a partial isometry satisfying, among others, the pentagon equation. In case of V being unitary we recover the Baaj-Skandalis multiplicative unitary of the discrete compact type. Relation to the pseudomultiplicative unitary approac...