K. Beanland

activity

20042026

most citedOn strictly singular operators between separable Banach spaces

7 citations · 24 across the 28 of their papers we have counts for

collaborators

34 papers

math.FA2026

Transfinite Schreier families and cardinal invariants

Kevin Beanland, Christian Rosendal

We study the dependence of the transfinite Schreier hierarchy on the choice of fundamental sequences for the countable limit ordinals. With each Schreier family we associate an int…

math.FA2025

Lower-Order Refinements of Greedy Approximation

Kevin Beanland, Hung Viet Chu, Thomas Schlumprecht +1

For two countable ordinals $α$ and $β$ , a basis of a Banach space $X$ is said to be $(α, β)$ -quasi-greedy if it is 1) quasi-greedy, 2) $S_{α}$ -unconditional but not $\mathc…

math.CO2023★ 1 cited

On Schreier-type Sets, Partitions, and Compositions

Kevin Beanland, Hung Viet Chu

A nonempty set $A \subset N$ is $ℓ$ -strong Schreier if $min A ⩾ ℓ ∣ A ∣ - ℓ + 1$ . We define a set of positive integers to be sparse if either the set has at most t…

math.FA2023

The depth of Tsirelson's norm

Kevin Beanland, Jędrzej Hodor

Tsirelson's norm $∥ \cdot ∥_{T}$ on $c_{00}$ is defined as the supremum over a certain collection of iteratively defined, monotone increasing norms $∥ \cdot ∥_{k}$ . For each positive…

math.FA2022

Schreier families and $F$ -(almost) greedy bases

Kevin Beanland, Hung Viet Chu

Let $F$ be a hereditary collection of finite subsets of $N$ . In this paper, we introduce and characterize $F$ -(almost) greedy bases. Given such a famil…

math.CO2022

Counting Unions of Schreier Sets

Kevin Beanland, Dmitriy Gorovoy, Jȩdrzej Hodor +1

A subset of positive integers $F$ is a Schreier set if it is non-empty and $∣ F ∣ ⩽ min F$ (here $∣ F ∣$ is the cardinality of $F$ ). For each positive integer $k$ , we define $k…