Perturbations of isometries between C(K)-spaces

Isometries between spaces of homogeneous polynomials

We derive Banach-Stone theorems for spaces of homogeneous polynomials. We show that every isometric isomorphism between the spaces of n-homogeneous approximable polynomials on real Banach spaces E and F is induced by an isometric isomorphism of E′ onto F ′. With an additional geometric condition we obtain the analogous result in the complex case. Isometries between spaces of n-homogeneous integ...

On the Structure of Isometries between Noncommutative L Spaces

We prove some structure results for isometries between noncommutative L spaces associated to von Neumann algebras. We find that an isometry T : L(M1) → L(M2) (1 ≤ p < ∞, p 6= 2) can be canonically expressed in a certain simple form whenever M1 has variants of Watanabe’s extension property [W2]. Conversely, this form always defines an isometry provided that M1 is “approximately semifinite” (defi...

Isometries for Ky Fan Norms Between Matrix Spaces

We characterize linear maps between different rectangular matrix spaces preserving Ky Fan norms.

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).