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A family is constructed of cardinality equal to the continuum, whose members are totally incomparable hereditarily indecomposable Banach spaces.
2000 Mathematics Subject Classification: 05D10, 46B03.
Given r ∈ (1, ∞), we construct a new L∞ separable Banach space which is lr saturated.
It is shown that for every 1 ≤ ξ < ω, two subspaces of the Schreier space generated by subsequences and , respectively, of the natural Schauder basis of are isomorphic if and only if and are equivalent. Further, admits a continuum of mutually incomparable complemented subspaces spanned by subsequences of . It is also shown that there exists a complemented subspace spanned by a block basis of , which is not isomorphic to a subspace generated by a subsequence of , for every ....
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