Abstract
AbstractLet K be either the real unit interval [0, 1] or the complex unit circle $${\mathbb {T}}$$
T
and let C(Y) be the space of all complex-valued continuous functions on a compact Hausdorff space Y. We prove that the isometry group of the algebra $$C^1(K,C(Y))$$
C
1
(
K
,
C
(
Y
)
)
of all C(Y)-valued continuously differentiable maps on K, equipped with the $$\Sigma $$
Σ
-norm, is topologically reflexive and 2-topologically reflexive whenever the isometry group of C(Y) is topologically reflexive.
Funder
Consejería de Economía, Innovación, Ciencia y Empleo, Junta de Andalucía
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Geometry and Topology,Algebra and Number Theory,Analysis
Reference30 articles.
1. Ancel, F.D., Singh, S.: Rigid finite dimensional compacta whose squares are manifolds. Proc. Am. Math. Soc. 87, 342–346 (1983)
2. Botelho, F., Jamison, J.E.: Surjective isometries on spaces of differentiable vector-valued functions. Stud. Math. 192, 39–50 (2009)
3. Cabello Sánchez, F., Molnár, L.: Reflexivity of the isometry group of some classical spaces. Rev. Mat. Iberoam. 18, 409–430 (2002)
4. Cambern, M.: Isometries of certain Banach algebras. Stud. Math. 25, 217–225 (1965)
5. Fleming, R.J., Jamison, J.E.: Isometries on Banach spaces: vol. 2. Vector-valued function spaces. In: Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Mathematics, vol. 138. Chapman & Hall/CRC, Boca Raton (2008)