Maji, Amit ; Sarkar, Jaydeb ; Sarkar, Srijan (2018) Toeplitz and asymptotic Toeplitz operators on H2(D)n Bulletin des Sciences Mathematiques, 146 . pp. 33-49. ISSN 0007-4497
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Official URL: https://doi.org/https://doi.org/10.1016/j.bulsci.2...
Related URL: http://dx.doi.org/https://doi.org/10.1016/j.bulsci.2018.03.005
Abstract
We initiate a study of Toeplitz operators and asymptotic Toeplitz operators on the Hardy space H2(D)n (over the unit polydisc Dn in Cn. Our main results on Toeplitz and asymptotic Toeplitz operators can be stated as follows: Let Tzi denote the multiplication operator on H2(D)n by the i-th coordinate function zi, i = 1,…,n, and let T be a bounded linear operator on H2(D)n. Then the following hold: (i) T is a Toeplitz operator (that is, T = PH2(D)nMϕ|H2(D)n, where Mϕ is the Laurent operator on L2(Tn) for some ϕ ∊ L∞(Tn)) if and only if T⁎ziTTzi = T for all i = 1,…,n. (ii) T is an asymptotic Toeplitz operator if and only if T = Toeplitz + compact. The case n = 1 is the well known results of Brown and Halmos, and Feintuch, respectively. We also present related results in the setting of vector-valued Hardy spaces over the unit disc.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Elsevier Science. |
| Keywords: | Toeplitz Operators; Hardy Space Over the Polydisc; Vector-Valued Hardy Spaces; Compact Operators; Quotient Spaces; Model Spaces |
| ID Code: | 140407 |
| Deposited On: | 22 Sep 2025 14:43 |
| Last Modified: | 22 Sep 2025 14:43 |
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