Some new properties and isometries on the unit spheres of generalized James spaces JpJp

This paper concerns the study of generalized James space JpJp. In this notation J2J2 is the well-known James space. We characterize surjective isometries of the unit sphere of JpJp. As a result, we answer Tingley’s problem affirmatively in JpJp and generalize Bellenot’s result to JpJp. Precisely we prove that JpJp admits only trivial surjective isometries.