Examples
For the spaces, the Pn is reflexive if and only if n < p. Thus, no is polynomially reflexive. ( is ruled out because it is not reflexive.)
Thus if space contains as a quotient space, it is not polynomially reflexive. This makes polynomially reflexive spaces rare.
The symmetric Tsirelson space is polynomially reflexive.
Read more about this topic: Polynomially Reflexive Space
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