| Date: | August 20, 2018 |
| Time: | 3:00pm |
| Location: | BLOC 220 |
| Speaker: | Ryan Causey, Miami University |
| Title: | Three and a half asymptotic properties |
| Abstract: | We introduce several isomorphic and isometric properties related to asymptotic uniform smoothness. These properties are analogues of p-smoothability, martingale type p, and equal norm martingale type p. We discuss distinctness, alternative characterizations, and renorming theorems for these properties.
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| Date: | August 21, 2018 |
| Time: | 3:00pm |
| Location: | BLOC 220 |
| Speaker: | Paul Müller, Johannes Kepler Universität Linz |
| Title: | Vector valued Hardy martingales and complex uniform convexity conditions on Banach spaces |
| Abstract: | We introduce a complex uniform convexity condition $\mathcal{ H }(q) $ on
a Banach space and show that it yields Davis and Garsia inequalities as well as
previsible projection estimates for vector valued Hardy martingales.
The talk is based on "A Decomposition for Hardy martingales III, Math
Proc. Camb. Phil. Soc. (2017)"
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| Date: | August 22, 2018 |
| Time: | 3:00pm |
| Location: | BLOC 220 |
| Speaker: | Richard Lechner, Johannes Kepler Universität Linz |
| Title: | Dimension dependence of factorization problems |
| Abstract: | Abstract:
For each $n\in\mathbb{N}$, let $(e_j)_{j=1}^n$ denote a normalized $1$-unconditional basis for the
$n$-dimensional Banach space $X_n$. We consider the following question: What is the smallest
possible dimension $N=N(n)$ such that the identity operator on $X_n$ factors through any operator
having large diagonal on $X_N$ ? For one- and two-parameter dyadic Hardy spaces and $SL^\infty$, we
improve the best previously known \emph{super-exponential} estimates for $N=N(n)$ to
\emph{polynomial} estimates.
References:
R. Lechner. Dimension dependence of factorization problems: Hardy spaces and $SL_n^\infty$. ArXiv
e-prints https://arxiv.org/abs/1802.02857, Feb. 2018.
R. Lechner. Dimension dependence of factorization problems: bi-parameter Hardy spaces. ArXiv
e-prints https://arxiv.org/abs/1802.05994, Feb. 2018. |
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