In this article, the known characterization of the surjective linear isometries of the Bochner space $L^p(\mu, H)$, for a $\sigma$-finite measure $\mu$ and an arbitrary Hilbert space $H$, in terms of regular set isomorphisms of the $\sigma$-algebra involved and strongly measurable families of surjective isometries of $H$, is extended to arbitrary measures.
CENGİZ, BAHATTİN (1999) "The Isometries of the Bochner Space L^p(\mu,H)," Turkish Journal of Mathematics: Vol. 23: No. 3, Article 4. Available at: https://journals.tubitak.gov.tr/math/vol23/iss3/4