Isometries on Banach algebras of vector-valued maps

2017/09/18 by Osamu Hatori, Hatori, Osamu, Shiho Oi +1
Mathematics · #46B04 #46E40 #46J10 #46J15 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.1709.05782

openalex publication_date 2017/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a unified approach to the study of isometries on algebras of vector-valued Lipschitz maps and those of continuously differentiable maps by means of the notion of admissible quadruples. We describe isometries on function spaces of some admissible quadruples that take values in unital commutative C^*-algebras. As a consequence we confirm the statement of \cite[Example 8]jp on Lipschitz algebras and show that isometries on such algebras indeed take the canonical form.

Related

• Isometries on Banach algebras of C(Y)-valued maps
• Isometries of absolute order unit spaces
• Spectral isometries on non-simple C*-algebras
• C*-Algebras Generated by Partial Isometries
• Complete isometries into C*-algebras