The quotient shapes of lp and Lp spaces

Sa？etak All lp spaces (over the same field), p ≠ ∞, have the finite quotient shape type of the Hilbert space l2. It is also the finite quotient shape type of all the subspaces lp(p'), p < p' ≤ ∞, as well as of all their direct sum subspaces F0N(p'), 1 ≤ p' ≤ ∞. Furthermore, their countable and finite quotient shape types coincide. Similarly, for a given positive integer, all Lp spaces (over the same field) have the finite quotient shape type of the Hilbert space L2, and their countable and finite quotient shape types coincide. Quite analogous facts hold true for the (special type of) Sobolev spaces (of all appropriate real functions)