An Elementary Proof of Nonexistence of Isometries between ℓpk and ℓqk

摘要

For k = 2, the two-dimensional coordinate spaces ℓ12 and ℓ∞2 are isometric. Consequently, results on computational complexity for one space can be transplanted to the other in a natural way. In this note, an elementary proof is given for the nonisometry between ℓpk and ℓqk for general k, p, and q.