Abstract
We give criteria of total incomparability for certain classes of mixed Tsirelson spaces. We show that spaces of the form \(T\left[ {\left( {\mathcal{M}_k ,\theta _k } \right)_{k = 1}^l } \right]\)with index \(i\left( {\mathcal{M}_k } \right)\) finite are either c 0 or \(\ell _p \) saturated for some p and we characterize when any two spaces of such a form are totally incomparable in terms of the index \(i\left( {\mathcal{M}_k } \right)\) and the parameter θ k . Also, we give sufficient conditions of total incomparability for a particular class of spaces of the form \(T\left[ {\left( {\mathcal{A}_k ,\theta _k } \right)_{k = 1}^\infty } \right]\) in terms of the asymptotic behaviour of the sequence \(\left\| {\sum\limits_{j = 1}^n {e_i } } \right\|\) where (e i is the canonical basis.
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Bernués, J., Pascual, J. On Total Incomparability of Mixed Tsirelson Spaces. Czech Math J 53, 841–859 (2003). https://doi.org/10.1023/B:CMAJ.0000024525.79869.ce
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DOI: https://doi.org/10.1023/B:CMAJ.0000024525.79869.ce