Isometries of Lipschitz type function spaces

Abstract

In this article, we describe isometries over the Lipschitz spaces under certain conditions. Indeed, we provide a unified proof for the main results of and in a more general setting. Finally, we extend our results for some other functions spaces like the space of vector‐valued little Lipschitz maps and pointwise Lipschitz maps.

Hermitian Operators and Isometries on Banach Algebras of Continuous Maps with Values in Unital Commutative C⁎-Algebras

“…Botelho and Jamison [10] studied isometries on 1 ([0, 1], ) with max ∈[0,1] {‖ ( )‖ + ‖ ( )‖ }. See also [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. Refer also to a book of Weaver [28].…”

A Remark on Isometries of Absolutely Continuous Spaces

“…where ϕ: Y ⟶ X and its inverse are absolutely continuous, and J is an absolutely continuous map from Y into the space of surjective linear isometries from V into W. Compare with [1], eorem 1.8 and [2], eorem 5.3.…”