arXiv subjects

Mo Javed

Publications and source records attributed to Mo Javed.

4 recordsLinked to original sources

arXiv2026

Characterization of paired and Toeplitz + Hankel operators on the polydisc

In this paper, we obtain a complete classification of Toeplitz + Hankel operators on the vector-valued Hardy space $H^2_{\mathcal{E}}(\mathbb{D}^n)$ over the polydisc $\mathbb{D}^n$ in $\mathbb{C}^n$ for $n\geq 1$. We also characterize the paired operators on $L^2(\mathbb{T}^n)$. Furthermore, we give a complete characterization for the class of essentially Toeplitz + essentially Hankel operators on the vector-valued Hardy space $H^2_{\mathcal{E}}(\mathbb{D})$ for finite-dimensional Hilbert space $\mathcal{E}$.

math.FA↗

arXiv2026

Partially isometric truncated and dual truncated Toeplitz operators

Let $\theta$ be a non-constant inner function and let $\phi=\overline{u}v$, where $u$ and $v$ are inner functions such that $v$ divides $\theta$. In this paper we characterize the partially isometric truncated Toeplitz operators $A_{\phi}$ and dual truncated Toeplitz operators $D_{\phi}$ with symbols of the form $\phi=\overline{u}v$. Along with that, we obtain a few more characterization results, including the space of extremal vectors for non-zero partially isometric truncated and dual truncated Toeplitz operators.

math.FA↗

arXiv2025

Invertibility of Bergman Toeplitz operators

In this paper, we establish the invertibility of the Berezin transform of the symbol as a necessary and sufficient condition for the invertibility of the Toeplitz operator on the Bergman space $L^2_a(\mathbb{D})$. More precisely, if ${\phi} = c g + d \bar{g}$, where $c,d\in\mathbb{C}$ and $g\in H^{\infty}(\mathbb{D})$, the space of all bounded analytic functions, then $T_{\phi}$ is invertible on $L^2_a(\mathbb{D})$ if and only if $\inf\limits_{z\in \mathbb{D}}\left|\widetilde{\,{\phi}}(z)\right|=\inf\limits_{z\in \mathbb{D}}|\phi(z)|>0$, where $\widetilde{\,{\phi}}$ is the Berezin transform of $\phi$.

math.FA↗

arXiv2024

Toeplitz algebra and Symbol map via Berezin transform on $H^2(\mathbb{D}^n)$

Let $\mathscr{T}(L^{\infty}(\mathbb{T}))$ be the Toeplitz algebra, that is, the $C^*$-algebra generated by the set $\{T_{\phi} : \phi\in L^{\infty}(\mathbb{T})\}$. Douglas's theorem on symbol map states that there exists a $C^*$-algebra homomorphism from $\mathscr{T}(L^{\infty}(\mathbb{T}))$ onto $L^{\infty}(\mathbb{T})$ such that $T_{\phi}\mapsto \phi$ and the kernel of the homomorphism coincides with commutator ideal in $\mathscr{T}(L^{\infty}(\mathbb{T}))$. In this paper, we use the Berezin transform to study results akin to Douglas's theorem for operators on the Hardy space $H^2(\mathbb{D}^n)$ over the open unit polydisc $\mathbb{D}^n$ for $n\geq 1$. We further obtain a class of bigger $C^*$-algebras than the Toeplitz algebra $\mathscr{T}(L^{\infty}(\mathbb{T}^n))$ for which the analog of symbol map still holds true.

math.FA↗