Trace of Multiplication Operator Restricted to Invariant Subspaces of some Weighted Bergman Space

Faruk Yılmaz

doi:10.17776/csj.1863606

Trace of Multiplication Operator Restricted to Invariant Subspaces of some Weighted Bergman Space

Abstract

Let ω be a logarithmically subharmonic weight that is radial and reproducing for the origin, and L_a^2 (D,ωdA) be the weighted Bergman space. Let f be a bounded holomorphic function on the open unit disc, I be a z-invariant subspace of L_a^2 (D,ωdA), and f(M_I) denotes the restriction to I of the multiplication operator M_f. This paper investigates the trace of the self-commutator of the operator f(M_I). More precisely, we compute the trace of the commutator [f(M_I )^*,f(M_I)] and show that it equals dim⁡(I⊝zI)∫_D |f^' (z)|^2 dA(z).

Keywords

Invariant subspaces, Multiplication operator, Weighted Bergman space

References

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Details

Primary Language

English

Subjects

Operator Algebras and Functional Analysis

Journal Section

Research Article

Authors

Faruk Yılmaz ^*
0000-0003-2742-7963
Türkiye

Publication Date

April 29, 2026

Submission Date

January 14, 2026

Acceptance Date

April 14, 2026

Published in Issue

Year 2026 Volume: 47 Number: 2

DOI

https://doi.org/10.17776/csj.1863606

IZ

https://izlik.org/JA29PM85EF

APA

Yılmaz, F. (2026). Trace of Multiplication Operator Restricted to Invariant Subspaces of some Weighted Bergman Space. Cumhuriyet Science Journal, 47(2), 361-365. https://doi.org/10.17776/csj.1863606

AMA

1.Yılmaz F. Trace of Multiplication Operator Restricted to Invariant Subspaces of some Weighted Bergman Space. CSJ. 2026;47(2):361-365. doi:10.17776/csj.1863606

Chicago

Yılmaz, Faruk. 2026. “Trace of Multiplication Operator Restricted to Invariant Subspaces of Some Weighted Bergman Space”. Cumhuriyet Science Journal 47 (2): 361-65. https://doi.org/10.17776/csj.1863606.

EndNote

Yılmaz F (April 1, 2026) Trace of Multiplication Operator Restricted to Invariant Subspaces of some Weighted Bergman Space. Cumhuriyet Science Journal 47 2 361–365.

IEEE

[1]F. Yılmaz, “Trace of Multiplication Operator Restricted to Invariant Subspaces of some Weighted Bergman Space”, CSJ, vol. 47, no. 2, pp. 361–365, Apr. 2026, doi: 10.17776/csj.1863606.

ISNAD

Yılmaz, Faruk. “Trace of Multiplication Operator Restricted to Invariant Subspaces of Some Weighted Bergman Space”. Cumhuriyet Science Journal 47/2 (April 1, 2026): 361-365. https://doi.org/10.17776/csj.1863606.

JAMA

1.Yılmaz F. Trace of Multiplication Operator Restricted to Invariant Subspaces of some Weighted Bergman Space. CSJ. 2026;47:361–365.

MLA

Yılmaz, Faruk. “Trace of Multiplication Operator Restricted to Invariant Subspaces of Some Weighted Bergman Space”. Cumhuriyet Science Journal, vol. 47, no. 2, Apr. 2026, pp. 361-5, doi:10.17776/csj.1863606.

Vancouver

1.Faruk Yılmaz. Trace of Multiplication Operator Restricted to Invariant Subspaces of some Weighted Bergman Space. CSJ. 2026 Apr. 1;47(2):361-5. doi:10.17776/csj.1863606

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Trace of Multiplication Operator Restricted to Invariant Subspaces of some Weighted Bergman Space

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