Dimension dependence of factorization problems

Description

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.

Period	22 Aug 2018
Event title	Workshop in Analysis and Probability Seminar, Texas A&M University, College Station, August 20-22, 2018
Event type	Conference
Location	United StatesShow on map