Georgios Tsikalas

activity

20212026

collaborators

11 papers

math.FA2026

Beurling Criteria for Reproducing Kernels

Shuaibing Luo, Scott McCullough, Georgios Tsikalas

A classical theorem due to Beurling-Lax-Halmos characterizes the invariant subspaces of the unilateral shift as ranges of isometric multiplication operators acting on the Hardy spa…

math.FA2026

When do Kernels Admit Characteristic Functions?

Caixing Gu, Shuaibing Luo, Georgios Tsikalas +1

A general framework for deriving characteristic functions for reproducing kernels that do not necessarily possess the complete Pick property was recently established by Bhattachary…

math.FA2026

Spectral Estimates over Multiply Connected Domains

Georgios Tsikalas

We consider the quantum analogue of a disk with $n$ pairwise disjoint circular holes. We establish a uniform upper bound for the associated spectral constant that is independent of…

math.FA2025

Operators with small Kreiss constants

Nikolaos Chalmoukis, Georgios Tsikalas, Dmitry Yakubovich

We investigate matrices satisfying the Kreiss condition $∥ (z I - T)^{- 1} ∥ \leq \frac{K}{∣ z ∣ - 1}, ∣ z ∣ > 1,$ with $K$ lying arbitrarily close to $1.$ We provide lower bo…

math.FA2024

The complete Pick property for pairs of kernels and Shimorin's factorization

Scott McCullough, Georgios Tsikalas

Let $(H_{k}, H_{ℓ})$ be a pair of Hilbert function spaces with kernels $k, ℓ$ . In a 2005 paper, Shimorin showed that a certain factorization condition on $(…

math.FA2023

Positivity conditions on the annulus via the double-layer potential kernel

Michael T. Jury, Georgios Tsikalas

We introduce and study a scale of operator classes on the annulus that is motivated by the $C_{ρ}$ classes of $ρ$ -contractions of Nagy and Foiaş. In particular, our classes…

math.FA2023

Denjoy-Wolff points on the bidisk via models

Michael T. Jury, Georgios Tsikalas

Let $F = (ϕ, ψ) : D^{2} \to D^{2}$ denote a holomorphic self-map of the bidisk without interior fixed points. It is well-known that, unlike the case with self-maps of the d…

math.FA2022

Interpolating sequences for pairs of spaces

Georgios Tsikalas

We characterize interpolating sequences for pairs of reproducing kernels $(s, ℓ)$ , where $s$ is a complete Pick factor of $ℓ .$ This answers a question of Aleman, Hartz, McCar…

math.FA2022

Subinner-free outer factorizations on an annulus

Georgios Tsikalas

Recent work of Aleman, Hartz, McCarthy and Richter generalizes the classical inner-outer factorization of Hardy space functions to the complete Pick space setting, establishing an…

math.FA2021

A von Neumann type inequality for an annulus

Georgios Tsikalas

Let $A_{r} = {r < ∣ z ∣ < 1}$ be an annulus. We consider the class of operators $F_{r} := {T \in B (H) : r^{2} T^{- 1} (T^{- 1})^{*} + T T^{*} \leq r^{2} + 1, σ (T) \subset A_{r}}$ a…

math.FA2021

A note on a spectral constant associated with an annulus

Georgios Tsikalas

Fix $R > 1$ and let $A_{R} = {1/ R \leq ∣ z ∣ \leq R}$ be an annulus. Also, let $K (R)$ denote the smallest constant such that $A_{R}$ is a $K (R)$ -spectral set for the bounded linear operator $…