The g-drazin inverse involving power commutativity

Chen H., Sheibani M., KÖSE H.

Filomat, cilt.34, sa.9, ss.2961-2969, 2020 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 34 Sayı: 9
  • Basım Tarihi: 2020
  • Doi Numarası: 10.2298/fil2009961c
  • Dergi Adı: Filomat
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.2961-2969
  • Anahtar Kelimeler: Additive property, Banach algebra, g-Drazin inverse, Perturbation
  • Ankara Üniversitesi Adresli: Evet

Özet

Let A be a complex Banach algebra. An element a ∈ A has g-Drazin inverse if there exists b ∈ A such that b = bab, ab = ba, a − a2b ∈ Aqnil . Let a, b ∈ Ad . If a3b = ba, b3a = ab, and a2adb = aadba, we prove that a + b ∈ Ad if and only if 1 + adb ∈ Ad . We present explicit formula for (a + b)d under certain perturbations. These extend the main results of Wang, Zhou and Chen (Filomat, 30(2016), 1185–1193) and Liu, Xu and Yu (Applied Math. Comput., 216(2010), 3652–3661).