dc.contributor.advisor | Schlumprecht, Thomas | |
dc.creator | Freeman, Daniel B. | |
dc.date.accessioned | 2010-10-12T22:31:32Z | |
dc.date.accessioned | 2010-10-14T16:02:36Z | |
dc.date.available | 2010-10-12T22:31:32Z | |
dc.date.available | 2010-10-14T16:02:36Z | |
dc.date.created | 2009-08 | |
dc.date.issued | 2010-10-12 | |
dc.date.submitted | August 2009 | |
dc.identifier.uri | https://hdl.handle.net/1969.1/ETD-TAMU-2009-08-7100 | |
dc.description.abstract | We study the relationship of dominance for
sequences and trees in Banach spaces. In the context of sequences,
we prove that domination of weakly null sequences is a uniform
property. More precisely, if $(v_i)$ is a normalized basic sequence
and $X$ is a Banach space such that every normalized weakly null
sequence in $X$ has a subsequence that is dominated by $(v_i)$, then
there exists a uniform constant $C\geq1$ such that every normalized
weakly null sequence in $X$ has a subsequence that is $C$-dominated
by $(v_i)$. We prove as well that if $V=(v_i)_{i=1}^\infty$
satisfies some general conditions, then a Banach space $X$ with
separable dual has subsequential $V$ upper tree estimates if and
only if it embeds into a Banach space with a shrinking FDD which
satisfies subsequential $V$ upper block estimates. We apply this
theorem to Tsirelson spaces to prove that for all countable ordinals
$\alpha$ there exists a Banach space $X$ with Szlenk index at most
$\omega^{\alpha \omega +1}$ which is universal for all Banach spaces
with Szlenk index at most $\omega^{\alpha\omega}$. | en |
dc.format.mimetype | application/pdf | |
dc.language.iso | en_US | |
dc.subject | upper estimates | en |
dc.subject | uniform estimates | en |
dc.subject | weakly null sequences | en |
dc.subject | Szlenk index | en |
dc.subject | universal space | en |
dc.subject | embedding into FDDs | en |
dc.subject | Efros-Borel structure | en |
dc.subject | analytic classes | en |
dc.title | Upper Estimates for Banach Spaces | en |
dc.type | Book | en |
dc.type | Thesis | en |
thesis.degree.department | Mathematics | en |
thesis.degree.discipline | Mathematics | en |
thesis.degree.grantor | Texas A&M University | en |
thesis.degree.name | Doctor of Philosophy | en |
thesis.degree.level | Doctoral | en |
dc.contributor.committeeMember | Johnson, William | |
dc.contributor.committeeMember | Larson, David | |
dc.contributor.committeeMember | Dahm, Fred | |
dc.type.genre | Electronic Dissertation | en |
dc.type.material | text | en |