arXiv subjects

Kritika Babbar

Publications and source records attributed to Kritika Babbar.

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 $θ$ be a non-constant inner function and let $ϕ=\overline{u}v$, where $u$ and $v$ are inner functions such that $v$ divides $θ$. In this paper we characterize the partially isometric truncated Toeplitz operators $A_ϕ$ and dual truncated Toeplitz operators $D_ϕ$ with symbols of the form $ϕ=\overline{u}v$. 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

Characteristic function of a power partial isometry

The celebrated Sz.-Nagy-Foiaş model theory says that there is a bijection between the class of purely contractive analytic functions and the class of completely non-unitary (c.n.u.) contractions modulo unitary equivalence. In this paper we provide a complete classification of the purely contractive analytic functions such that the associated contraction is a c.n.u. power partial isometry. As an application of our findings, we determine a class of contractive polynomials such that the associated c.n.u. power partial isometry is of the explicit diagonal form $S \oplus N \oplus C$, where $S$ and $C^*$ are unilateral shifts and $N$ is nilpotent. Finally, we obtain a characterization of operator-valued symbols for which the corresponding Toeplitz operator on vector-valued Hardy space is a partial isometry.

math.FA↗

arXiv2025

Power partial isometries

In this paper we obtain a complete characterization of reducing, invariant, and hyperinvariant subspaces for the completely non-unitary component of a power partial isometry. In particular, precise characterization of reducing, invariant, and hyperinvariant subspaces of a truncated shift operator has been achieved.

math.FA↗