Tsirelson space

A specific example of a reflexive Banach space (cf. Reflexive space) which does not contain an imbedded -space or an imbedded -space. On the other hand, the classical Banach spaces, such as the spaces of equivalence classes of measurable functions whose -th powers are integrable and the spaces of continuous scalar-valued functions on with the supremum norm, all do contain a copy of or , and so do all Orlicz spaces (cf. Orlicz space).

For a selection of results concerning Banach spaces which do contain or see [a3], Sect. 2e.

References

[a1]	B.S. Tsirelson, "Not every Banach space contains an imbedding of or " Funct. Anal. Appl. , 8 : 2 (1974) pp. 138–141 Funkts. Anal. Prilozhen. , 8 : 2 (1974) pp. 57–60
[a2]	P.G. Casazza, Th.J. Shura, "Tsirelson's space" , Lect. notes in math. , 1363 , Springer (1989)
[a3]	J. Lindenstrauss, L. Tzafriri, "Classical Banach spaces" , 1. Sequence spaces , Springer (1977)
[a4]	D. van Dulst, "Characterizations of Banach spaces not containing " , CWI (1989)