Das, Susmita ; Sarkar, Jaydeb (2022) Tridiagonal shifts as compact + isometry Archiv der Mathematik, 119 (5). pp. 507-518. ISSN 0003-889X
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Official URL: https://doi.org/10.1007/s00013-022-01780-8
Related URL: http://dx.doi.org/10.1007/s00013-022-01780-8
Abstract
Let {aₙ}n≥0 and {bₙ}n≥0 be sequences of scalars. Suppose aₙ ≠ 0 for all n ≥ 0. We consider the tridiagonal kernel (also known as band kernel with bandwidth one) as: k(z, w) = ∞∑n=0 ((aₙ + bₙz)zⁿ)((aₙ + bₙw)wⁿ) (z, w ∈ where D = {z ∈ C : |z| < 1}. Denote by 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: Mz = compact + isometry if and only if |bₙ/aₙ − bₙ₊₁/aₙ₊₁| → 0 and |aₙ/aₙ₊₁| → 1.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Birkhauser-Verlag. |
| Keywords: | Tridiagonal kernels; Perturbations; Compact operators; Isometries; Shifts. |
| ID Code: | 140591 |
| Deposited On: | 29 Dec 2025 11:47 |
| Last Modified: | 29 Dec 2025 11:47 |
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