Results Math 72 (2017), 537–554
2017 Springer International Publishing
published online February 25, 2017
Results in Mathematics
Real-Multilinear Isometries on Function
Juan J. Font and Maliheh Hosseini
Abstract. Let A
be function algebras (or more generally, dense
subspaces of uniformly closed function algebras) on locally compact Haus-
dorﬀ spaces X
, respectively, and let Y be a locally compact
Hausdorﬀ space. A k-real-linear map T : A
× ··· × A
called a real-multilinear (or k-real-linear) isometry if
) ∈ A
where · denotes the supremum norm. In this paper we study such
maps and obtain generalizations of basically all known results concerning
multilinear and real-linear isometries on function algebras.
Mathematics Subject Classiﬁcation. Primary 46J10, 47B38,
Keywords. Function algebra, real-multilinear isometry,
Choquet boundary, Bishop’s Lemma, uniform algebra.
Let X be a locally compact Hausdorﬀ space and let C
is compact) denote the Banach space of complex-valued continuous functions
deﬁned on X vanishing at inﬁnity, endowed with the supremum norm ·.
The classical Banach-Stone theorem gave the ﬁrst characterization of surjec-
tive linear isometries between C(X)-spaces as weighted composition operators
Research of J.J. Font was partially supported by Spanish Government (MTM2016-77143-
P), Universitat Jaume I (Projecte P11B2014-35) and Generalitat Valenciana (Projecte
This work was partially supported by a grant from the Simons Foundation.