On extension of isometries between unit spheres of Lp(μ) and Lp(ν,H) (1<p≠2, H is a Hilbert space)

In this paper, we introduce a new class of mapping: p-affinely orthogonal mapping, obtain some relations with isometric mapping, give some sufficient conditions under which an isometric mapping from unit sphere of Lp(μ) into (or onto) that of another Banach space can be extended to be a linear isometry on the whole space, as well as show that any into (or onto) isometric mapping between the spheres of Lp(μ) and Lp(ν,H) (11) type spaces, Sci. China Ser. A 46 (3) (2003) 333–338] and [J. Wang, On extension of isometries between unit spheres of ALp-spaces (0