Linear isometries between certain subspaces of continuous vector-valued functions

Linear Surjective Isometries Between Vector-Valued Function Spaces

“…The result (1) follows the same line of reasoning as previous results [1,6,18,25,28]. On the other hand, (2) and (3) seem to exhibit a relatively new variant in that their assumptions are involved in the topology of underlying spaces X and Y (see [33] and a paper by K. Kawamura and Miura, 'Real-linear surjective isometries between function spaces,' which has been submitted for publication).…”

“…Some of the previous works study sufficient conditions that guarantee the condition 'ϕ η 1 = ϕ η 2 ' from which we conclude that T is a generalized weighted composition operator. These conditions have generally been stated in terms of some separation properties of the subspaces A and B. Theorem 3.4 is a result in this direction and its proof follows arguments given in [1,10,18]. For a subspace A of C(X, E), we consider the following condition.…”

“…Theorem 3.3 (Cf. [1,10,18]). Assume that E is strictly convex and reflexive, and assume, further, that A satisfies Condition (S1), Condition (S3) and Condition (ext).…”

“…The following condition, or its variants, sometimes replaces Condition (S1) and Condition (S2) (see [1,18]).…”

Isomorphisms of spaces with large distortion

“…Historically, the property of a space being strictly convex has been part of the hypotheses in many of the vector‐valued Banach–Stone theorems, including that of Jerison mentioned above, see for instance .…”