Isometric classification of Sobolev spaces on graphs

• Autorzy: M. I. Ostrovskii
• Języki publikacji: EN

Abstrakty

EN

Isometric Sobolev spaces on finite graphs are characterized. The characterization implies that the following analogue of the Banach-Stone theorem is valid: if two Sobolev spaces on 3-connected graphs, with the exponent which is not an even integer, are isometric, then the corresponding graphs are isomorphic. As a corollary it is shown that for each finite group 𝒢 and each p which is not an even integer, there exists n ∈ ℕ and a subspace $L ⊂ ℓⁿ_{p}$ whose group of isometries is the direct product 𝒢 × ℤ₂.

Kategorie tematyczne

• 52A21: Finite-dimensional Banach spaces (including special norms, zonoids, etc.)
• 46B04: Isometric theory of Banach spaces
• 05C40: Connectivity

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2007
• Tom: 109
• Numer: 2
• Strony: 287-295

Daty

wydano

2007

Twórcy

autor

M. I. Ostrovskii

• Department of Mathematics and Computer Science, St. John's University, 8000 Utopia Parkway, Queens, NY 11439, U.S.A.

Identyfikatory

DOI

10.4064/cm109-2-10