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- W4226054296 abstract "Let ${a_n}_{ngeq 0}$ and ${b_n}_{ngeq 0}$ be sequences of scalars. Suppose $a_n neq 0$ for all $n geq 0$. We consider the tridiagonal kernel (also known as band kernel with bandwidth one) as [ k(z, w) = sum_{n=0}^infty ((a_n + b_n z)z^n) overline{(({a}_n + {b}_n {w}) {w}^n)} qquad (z, w in mathbb{D}), ] where $mathbb{D} = {z in mathbb{C}: |z| < 1}$. Denote by $M_z$ the multiplication operator on the reproducing kernel Hilbert space corresponding to the kernel $k$. Assume that $M_z$ is left-invertible. We prove that $M_z =$ compact $+$ isometry if and only if $|frac{b_n}{a_n}-frac{b_{n+1}}{a_{n+1}}|rightarrow 0$ and $|frac{a_n}{a_{n+1}}| rightarrow 1$." @default.
- W4226054296 created "2022-05-05" @default.
- W4226054296 creator A5059577807 @default.
- W4226054296 creator A5067138593 @default.
- W4226054296 date "2021-11-07" @default.
- W4226054296 modified "2023-09-26" @default.
- W4226054296 title "Tridiagonal shifts as compact + isometry" @default.
- W4226054296 doi "https://doi.org/10.48550/arxiv.2111.04180" @default.
- W4226054296 hasPublicationYear "2021" @default.
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