Chao Zu

activity

20232026

M_{θ, φ}

-type submodules

1 citations · 2 across the 18 of their papers we have counts for

collaborators

18 papers

math.FA2026

Radial Convergence along Decreasing Coordinate Radii in \texorpdfstring{$H^\infty(\T^\infty)$}{H-infinity(T-infinity)}

Jiawei Sun, Chao Zu, Yufeng Lu

Aleman, Olsen, and Saksman asked whether radial convergence may fail for bounded analytic functions on the infinite-dimensional polydisc when every radial point has non-increasing…

math.FA2026

On the Spectra of Multiplicative Hilbert Operator on Bergman Spaces of Dirichlet Series

Tengfei Ma, Yufeng Lu, Chao Zu

For $α > 1$ , we study the weighted multiplicative Hilbert operator \[ (T_αf)(s) = \int_{1/2}^{\infty} f(t)\bigl(ζ(s+t)^α-1\bigr) \left(t-\frac12\right)^{α-1}\,dt \] on the Hilbertian…

math.FA2026

Verblunsky coefficients, CMV matrices and numerical invariants of homogeneous bidisc submodules

Yufeng Lu, Chao Zu

Let $[p]$ be the principal submodule generated by a polynomial in $H^{2} (D^{2})$ . For homogeneous $p$ , the homogeneous slices of $[p]$ admit a weighted OPUC model in which the…

math.FA2026

Strict Monotonicity of Numerical Invariants for the Submodules $[(z - w)^{k}]$ in $H^{2} (D^{2})$

Yin Liu, Yufeng Lu, Chao Zu

For $k \geq 1$ , let $M_{k} = [(z - w)^{k}] \subset H^{2} (D^{2})$ . We first determine the banded Toeplitz matrices associated with the homogeneous components of $M_{k}$ , together with explic…

math.FA2026

Corona theorem for the quaternionic Hardy space

Zhaopeng Lin, Yufeng Lu, Chao Zu

The finite-generator corona theorem for bounded slice regular functions on the quaternionic unit ball was recently established by Colombo, Pozzi, Sabadini, and Wick. In the present…

math.FA2026

Block Repetition of Numerical Invariants for the Submodules $[z^{k} - w^{k}]$ in $H^{2} (D^{2})$

Yin Liu, Yufeng Lu, Chao Zu

For $k \geq 2$ , let $M_{k} = [z^{k} - w^{k}]$ be the principal homogeneous submodule of the Hardy space over the bidisk. We determine Yang's complete sequence of numerical invariants and prove…

math.FA2026

Slice Regular Composition Operators on Quaternionic Fock Spaces via Matrix Realization

Zhaopeng Lin, Yufeng Lu, Chao Zu

We characterize the boundedness and compactness of slice regular composition operators between quaternionic Fock spaces for the full range $0<p,q<\infty$, without assuming that t…

math.FA2026

A Fourier Criterion for the Toeplitzness of Operators on Fock Spaces

Zhaopeng Lin, Yufeng Lu, Chao Zu

We give a Fourier criterion for the Toeplitzness of bounded operators on Fock spaces, where Toeplitzness means representability as a Toeplitz operator with a bounded measurable sym…

math.FA2026

On numerical invariants for submodules $[(z - w)^{2}]$ in $H^{2} (D^{2})$

Yin Liu, Yufeng Lu, Chao Zu

In this paper, we study numerical invariants associated with a homogeneous submodule of the Hardy module over the bidisk. We focus on the submodule generated by the polynomial $(z-…

math.FA2026

Compactness of products and commutators of inner projections

Peiran Zhang, Roumei Tian, Yufeng Lu +2

In this paper, we study the compactness of the product and the commutator of two inner projections on the Hardy spaces over the unit disk and the polydisc. For the single-variable…

math.FA2026

Spectral properties of Toeplitz operators with harmonic function symbols on the Bergman space

Puyu Cui, Yufeng Lu, Rongwei Yang +1

This paper investigates the spectral properties of Toeplitz operators on the Bergman space of unit disk. We present an integral representation of $T_{z^{m}}^{*}$ , which establishes a…

math.FA2026

Spectral dynamics for the infinite dihedral group and the lamplighter group

Chao Zu, Yixin Yang, Yufeng Lu

For a tuple $A = (A_{0}, A_{1}, \dots, A_{n})$ of elements in a Banach algebra $B$ , its projective (joint) spectrum $p (A)$ is the collection of $z \in P^{n}$ such that $A(z)…

math.FA2026★ 1 cited

A geometric approach to the compressed shift operator on the Hardy space over the bidisk

Yufeng Lu, Yixin Yang, Chao Zu

This paper studies the compressed shift operator $S_{z}$ on the Hardy space over the bidisk via the geometric approach. We calculate the spectrum and essential spectrum of $S_{z}$ on t…

math.FA2026

Nuclear Toeplitz operators between Fock spaces

Tengfei Ma, Yufeng Lu, Chao Zu

We characterize the nuclearity of Toeplitz operators $T_{μ} : F_{α}^{p} \to F_{α}^{q}$ with Borel measure symbols for $1 \leq p, q \leq \infty$ . For positive measures $μ$ and $q \leq p$ , we provi…

math.FA2026

Toeplitz Operators on Quaternionic Fock Spaces

Zhaopeng Lin, Yufeng Lu, Chao Zu

We characterize boundedness and compactness of Toeplitz operators on quaternionic Fock spaces with positive measure symbols and slice-function symbols in $\mathrm{BMO}^1$. For po…

math.FA2025★ 1 cited

Hilbert-Schmidtness of the $M_{θ, φ}$ -type submodules

Chao Zu, Yufeng Lu

Let $θ (z), φ (w)$ be two nonconstant inner functions and $M$ be a submodule in $H^{2} (D^{2})$ . Let $C_{θ, φ}$ denote the composition operator on $H^{2} (D^{2})$ defined by $C…

math.FA2025

Notes on a special order on $Z^{\infty}$

Jiawei Sun, Chao Zu, Yufeng Lu

In 1958, Helson and Lowdenslager extended the theory of analytic functions to a general class of groups with ordered duals. In this context, analytic functions on such a group $G$ …

math.FA2023

Which hyponormal block Toeplitz operators are either normal or analytic?

Senhua Zhu, Yufeng Lu, Chao Zu

In this paper, we continue Curto-Hwang-Lee's work to study the connection between hyponormality and subnormality for block Toeplitz operators acting on the vector-valued Hardy spac…

Radial Convergence along Decreasing Coordinate Radii in \texorpdfstring{$H^\infty(\T^\infty)$}{H-infinity(T-infinity)}

On the Spectra of Multiplicative Hilbert Operator on Bergman Spaces of Dirichlet Series

Verblunsky coefficients, CMV matrices and numerical invariants of homogeneous bidisc submodules

Strict Monotonicity of Numerical Invariants for the Submodules [(z−w)k] in H2(D2)

Corona theorem for the quaternionic Hardy space

Block Repetition of Numerical Invariants for the Submodules [zk−wk] in H2(D2)

Slice Regular Composition Operators on Quaternionic Fock Spaces via Matrix Realization

A Fourier Criterion for the Toeplitzness of Operators on Fock Spaces

On numerical invariants for submodules [(z−w)2] in H2(D2)

Compactness of products and commutators of inner projections

Spectral properties of Toeplitz operators with harmonic function symbols on the Bergman space

Spectral dynamics for the infinite dihedral group and the lamplighter group

A geometric approach to the compressed shift operator on the Hardy space over the bidisk

Nuclear Toeplitz operators between Fock spaces

Toeplitz Operators on Quaternionic Fock Spaces

Hilbert-Schmidtness of the Mθ,φ​-type submodules

Notes on a special order on Z∞

Which hyponormal block Toeplitz operators are either normal or analytic?

Strict Monotonicity of Numerical Invariants for the Submodules $[(z - w)^{k}]$ in $H^{2} (D^{2})$

Block Repetition of Numerical Invariants for the Submodules $[z^{k} - w^{k}]$ in $H^{2} (D^{2})$

On numerical invariants for submodules $[(z - w)^{2}]$ in $H^{2} (D^{2})$

Hilbert-Schmidtness of the $M_{θ, φ}$ -type submodules

Notes on a special order on $Z^{\infty}$