## Workshop in Analysis and Probability Seminar

**Date: ** August 22, 2018

**Time: ** 3:00PM - 3:50PM

**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.