An Elementary Proof of Nonexistence of Isometries between ℓpk and ℓqk

For k = 2, the two-dimensional coordinate spaces ℓ
1
²
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 ℓ
p
^k
and ℓ
q
^k
for general k, p, and q.