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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
In the last section, we deal with the spectrum of a $k^{th}$-order slant Toeplitz operator on $L^2(\mathbb{T}^n)$ and investigate the conditions for such an operator to be an isometry, hyponormal or normal.
📌 3 Key Takeaways
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Objective & Hypothesis:This paper discusses several structural and fundamental properties of the $k^{th}$-order slant Toeplitz operators on the Lebesgue space of the $n$- torus $\mathbb{T}^n$, for integers $k\geq 2$ and $n\geq 1$.
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Key Findings & Data:We obtain certain equivalent conditions for the commutativity and essential commutativity of these operators.
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Conclusion & Impact:In the last section, we deal with the spectrum of a $k^{th}$-order slant Toeplitz operator on $L^2(\mathbb{T}^n)$ and investigate the conditions for such an operator to be an isometry, hyponormal or normal.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:commutativity · Lebesgue space · slant Toeplitz operators
Abstract
This paper discusses several structural and fundamental properties of the $k^{th}$-order slant Toeplitz operators on the Lebesgue space of the $n$- torus $\mathbb{T}^n$, for integers $k\geq 2$ and $n\geq 1$. We obtain certain equivalent conditions for the commutativity and essential commutativity of these operators. In the last section, we deal with the spectrum of a $k^{th}$-order slant Toeplitz operator on $L^2(\mathbb{T}^n)$ and investigate the conditions for such an operator to be an isometry, hyponormal or normal.
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Cite This Article
DATT, G., PANDEY, S. K. (2022). Multivariate analogue of slant Toeplitz operators. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 3, 678–691. https://ajindex.com/articles/529502