Article Dans Une Revue Linear and Multilinear Algebra Année : 2016

Quasi-range-compatible affine maps on large operator spaces

Résumé

Let U and V be finite-dimensional vector spaces over an arbitrary field, and S be a subset of the space L(U,V) of all linear maps from U to V. A map F:SV is called range-compatible when it satisfies F(s)im(s) for all sS; it is called quasi-range-compatible when the condition is only assumed to apply to the operators whose range does not include a fixed 1-dimensional linear subspace of V. Among the range-compatible maps are the so-called local maps ss(x) for fixed xU. Recently, the range-compatible group homomorphisms on S were classified when S is a linear subspace of small codimension in L(U,V). In this work, we consider several variations of that problem: we investigate range-compatible affine maps on affine subspaces of linear operators; when S is a linear subspace, we give the optimal bound on its codimension for all quasi-range-compatible homomorphisms on S to be local. Finally, we give the optimal upper bound on the codimension of an affine subspace S of L(U,V) for all quasi-range-compatible affine maps on it to be local.

Dates et versions

hal-01690912 , version 1 (23-01-2018)

Identifiants

Citer

Clément de Seguins Pazzis, Clément de Seguins Pazzis. Quasi-range-compatible affine maps on large operator spaces. Linear and Multilinear Algebra, 2016, 64 (6), pp.1056 - 1085. ⟨10.1080/03081087.2015.1071316⟩. ⟨hal-01690912⟩
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