The strongest forms of Banach-Stone theorem to C₀(K, lⁿ_p) spaces for all n ≥ 3 and p close to 2

Autor(es)

Galego, Eloi Medina

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Analysis and Applications; v. 541, n. 2, p. 15-pg., 2024-08-01.

Resumo

Fix n >= 3 an integer and consider X = l (n )(p) the real finite n- dimensional classical Banach space with 1 < p < oo. Put lambda ( X ) = 2 (1 -1) (/p) if 1 < p <= 2 and lambda ( X ) = 2 (1 /p) if p >= 2. It is proven that there exists 0 < epsilon < 1 such that if p belongs to the open interval (2 - epsilon, 2 + epsilon ), then there is delta > 0 so that whenever K and S are locally compact Hausd orff spaces and T is a linear isomorphism from C-0(K, X) onto C-0(S, 0 ( S, X ) satisfying ||T || ||T-1|| <= (X ) + delta, then K and S are homeomorphic. This result provides the strongest forms of Banach-Stone theorem to C-0(K, l(p)(n)) spaces for all n >= 3 and p close to 2. It is an extension of the only case known so far (p = 2) which was obtained in 2019. Its proof ended up being a sample of how to rely on the geometry of the Hilbert spaces l (n)(2) to get new geometric information about other l(p)(n) spaces when p is near enough to 2. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies. (AU)

• Processo FAPESP: 23/12916-1 - Geometria de espaços de Banach
• Beneficiário: Valentin Raphael Henri Ferenczi
• Modalidade de apoio: Auxílio à Pesquisa - Temático