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

Yılmaz F.

CUMHURIYET SCIENCE JOURNAL, cilt.47, sa.2, ss.361-365, 2026 (TRDizin)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 47 Sayı: 2
  • Basım Tarihi: 2026
  • Doi Numarası: 10.17776/csj.1863606
  • Dergi Adı: CUMHURIYET SCIENCE JOURNAL
  • Derginin Tarandığı İndeksler: TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.361-365
  • Ankara Yıldırım Beyazıt Üniversitesi Adresli: Evet

Özet


Let 𝜔 be a logarithmically subharmonic weight the is radial and reproducing at the origin, and 𝐿2 (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 𝐿2 (𝔻, 𝜔𝑑𝐴), and 𝑓(𝑀𝐼) denotes the restriction of the multiplication operator 𝑀_f to 𝐼. This paper investigates the trace of the self-commutator of the operator 𝑓(𝑀𝐼). More precisely, we compute the trace of the commutator [𝑓(𝑀𝐼)∗, 𝑓(𝑀𝐼)] and show that it equals to dim⁡(𝐼 ⊝ 𝑧𝐼)∫𝔻|𝑓′(𝑧)|2𝑑𝐴(𝑧).