arXiv subjects

Buket Can Bahadır

Publications and source records attributed to Buket Can Bahadır.

3 recordsLinked to original sources

arXiv2026

Tame Factorization Property I

We introduce the \emph{tame factorization property} for triples of Fréchet spaces: a triple $(E,G,F)$ has the tame factorization property, denoted by $(E,G,F) \in \mathfrak{TF}$, if there exists a nondecreasing function $S:\mathbb{N}\to\mathbb{N}$ such that every operator from $E$ to $F$ factoring through $G$ is $S$-tame. We give a complete characterization of $\mathfrak{TF}$ in terms of operator seminorm estimates. We specialize this characterization to triples in which one or more of the spaces are Köthe spaces, putting explicit conditions on the Köthe matrices, and we describe how $\mathfrak{TF}$ behaves under projective tensor products of Köthe spaces. Finally, we show that a triple of Köthe spaces has the tame factorization property if and only if the family of operators that factor as products of two quasi-diagonal operators is tame.

math.FA↗

arXiv2026

Tame Factorization Property II

We investigate the relationship between the tame factorization property, denoted by $\mathfrak{TF}$ and introduced in the companion paper \cite{CDI}, and the DN-$Ω$ type linear topological invariants of Fréchet spaces. Combining the basic properties of $\mathfrak{TF}$ with known characterizations of tameness and boundedness, we obtain several results identifying the triples of Fréchet spaces that possess $\mathfrak{TF}$. We further exhibit examples showing that tame factorization property is a strictly weaker condition than tameness, indeed, we construct triples possessing $\mathfrak{TF}$ none of whose individual pairs are tame. We then investigate triples consisting of an arbitrary Fréchet space $X$, a nuclear Fréchet space $Y$ satisfying the properties $\underline{DN}$ and $Ω$, and a power series space of finite type $Λ_1(\mathcal{E})$ or infinite type $Λ_\infty(\mathcal{E})$. We show that requiring such a triple to possess the tame factorization property $\mathfrak{TF}$ characterizes the corresponding linear topological invariants of $X$; in some cases this holds without any restriction on $Y$, while in others it requires the coincidence of the approximate diametral dimension of $Y$ with that of $Λ_1(\mathcal{E})$ or $Λ_\infty(\mathcal{E})$.

math.FA↗

arXiv2025

On the Tameness of Power Series Space Pairs

In this paper, it is shown that the tameness of the Köthe space pair $(λ^p(A),λ^q(B))$ is determined solely by the tameness of the family of quasi-diagonal operators defined between the pair of spaces. We use this tool to fill the gaps in characterization of pairs of power series spaces, adding to the previously established results of Dubinsky, Vogt, Nyberg and etc., and summarize this complete characterization in Table 1. As a result, we also show that the range of every continuous tame operator defined between power series spaces of infinite type has a basis.

math.FA↗