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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Under supplementary assumptions, we find necessary and sufficient condition that the product $A_\Phi A_\Psi$ is itself a matrix valued truncated Toeplitz operator.
📌 3 Key Takeaways
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Objective & Hypothesis:Let $A_\Phi$ be a matrix valued truncated Toeplitz operator -- the compression of multiplication operator to the vector valued model space $H^2(E)\ominus \Theta H^2(E)$, where $\Theta$ is a matrix valued non constant inner function.
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Key Findings & Data:Let $A_\Phi$ be a matrix valued truncated Toeplitz operator -- the compression of multiplication operator to the vector valued model space $H^2(E)\ominus \Theta H^2(E)$, where $\Theta$ is a matrix valued non constant inner function.
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Conclusion & Impact:Under supplementary assumptions, we find necessary and sufficient condition that the product $A_\Phi A_\Psi$ is itself a matrix valued truncated Toeplitz operator.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:model spaces · truncated Toeplitz operator · inner function
Abstract
Let $A_\Phi$ be a matrix valued truncated Toeplitz operator -- the compression of multiplication operator to the vector valued model space $H^2(E)\ominus \Theta H^2(E)$, where $\Theta$ is a matrix valued non constant inner function. Under supplementary assumptions, we find necessary and sufficient condition that the product $A_\Phi A_\Psi$ is itself a matrix valued truncated Toeplitz operator.
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Cite This Article
Khan, M. A. (2022). Product of matrix valued truncated Toeplitz operators. Hacettepe Journal of Mathematics and Statistics, Volume: 51 Issue: 3. https://doi.org/10.15672/hujms.883318