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Nazlı Doğan

Publications and source records attributed to Nazlı Doğan.

8 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↗
arXiv2026

The Rhaly Operators on Köthe Spaces

We introduce and study the Rhaly operator on Köthe spaces, with a primary focus on understanding its well-definedness, continuity, and compactness. We especially examine operators acting on power series spaces of both infinite and finite type. In the sequel, we provide integral representations for the Rhaly operator on the space of entire functions $H(\mathbb{C})$ and the space of holomorphic functions on the unit disc $H(\mathbb{D})$. We also investigate the topologizability and power boundedness of the Rhaly operators, which leads to findings about their mean ergodicity, uniform mean ergodicity, and Cesàro boundedness.

math.FA↗
arXiv2024

Toeplitz Operators Defined between Köthe Spaces

The aim of this paper is to define Toeplitz operators between Köthe spaces, especially power series spaces. We determine the conditions for continuity and compactness of these operators. We define the concept of S-tameness of a family of continuous operators. We construct some conditions on S-tameness for the families consisting of Toeplitz operators.

math.FA↗
arXiv2024

Hankel Operators Defined Between Köthe Spaces

This paper is about the operators defined between Köthe spaces whose associated matrix is a Hankel matrix. After demonstrating how these operators are defined, the conditions for continuity and compactness of these operators are constructed. It is shown that the backward and forward shift operators are mean ergodic and Cesàro bounded by establishing a relationship between the backward and forward shift operators and Hankel and Toeplitz operators on power series spaces.

math.FA↗
arXiv2022

On Power Series Subspaces of Certain Nuclear Frechet Spaces

The diametral dimension, $Δ(E)$, and the approximate diametral dimension, $δ(E)$ of an element $E$ of a large class of nuclear Fréchet spaces are set theoretically between the corresponding invariant of power series spaces $Λ_{1}(\varepsilon)$ and $Λ_{\infty}(\varepsilon)$ for some exponent sequence $\varepsilon$. Aytuna et al., \cite{AKT2}, proved that $E$ contains a complemented subspace which is isomorphic to $Λ_{\infty}(\varepsilon)$ provided $Δ(E)=Δ( Λ_{\infty}(\varepsilon))$ and $\varepsilon$ is stable. In this article, we will consider the other extreme case and we proved that in this large family, there exist nuclear Fréchet spaces, even regular nuclear Köthe spaces, satisfying $Δ(E)=Δ(Λ_{1}(\varepsilon))$ such that there is no subspace of $E$ which is isomorphic to $Λ_{1}(\varepsilon)$.

math.FA↗
arXiv2020

Some Remarks on Diametral Dimension and Approximate Diametral Dimension of Certain Nuclear Fréchet Spaces

The diametral dimension, $Δ(E)$, and the approximate diametral dimension, $δ(E)$, of a nuclear Fréchet space $E$ which satisfies $\underline{DN}$ and $Ω$, is related to power series spaces $Λ_{1}(\varepsilon)$ and $Λ_{\infty}\left(\varepsilon\right)$ for some exponent sequence $\varepsilon$. In this article, we examine a question of whether $δ(E)$ must coincide with that of a power series space if $Δ(E)$ does the same, and vice versa. In this regard, we first show that this question has an affirmative answer in an infinite type case by proving the fact that $Δ(E)=Δ\left(Λ_{\infty} (\varepsilon)\right)$ if and only if $δ(E)= δ(Λ_{\infty}(\varepsilon))$. Then we consider the question in the finite type case and, among other things, we prove that $δ(E)=δ\left(Λ_{1} (\varepsilon)\right)$ if and only if $Δ(E)= Δ(Λ_{1}(\varepsilon))$ and $E$ has a prominent bounded subset.

math.FA↗