Original scientific paper
https://doi.org/10.21857/9xn31cr62y
The quotient shapes of lp and Lp spaces
Nikica Uglešić
; Veli Råt, Dugi Otok, Hrvatska
Abstract
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).
Keywords
Normed (Banach, Hilbert vectorial) space; quotient normed space; lp space; Lp space; Sobolev space; (algebraic) dimension; (infinite) cardinal; (general) continuum hypothesis; quotient shape
Hrčak ID:
206201
URI
Publication date:
28.9.2018.
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