We study minimality properties of partly modified mixed Tsirelson spaces. A Banach space with a normalized basis (ek) is said to be subsequentially minimal if for every normalized block basis (xk) of (ek), there is a further block basis (yk) of (x k) such that (yk) is equivalent to a subsequence of (ek). Sufficient conditions are given for a partly modified mixed Tsirelson space to be subsequentially minimal, and connections with Bourgain's l1 -index are established. It is also shown that a large class of mixed Tsirelson spaces fails to be subsequentially minimal in a strong sense.
|Original language||English (US)|
|Number of pages||31|
|State||Published - 2008|
- Partly modified mixed Tsirelson spaces
- Subsequential minimality
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