REGULARIZED TRACE ON SEPARABLE BANACH SPACES

GÜL E., Gill T.

Turkish World Mathematical Society Journal of Applied and Engineering Mathematics, cilt.13, sa.1, ss.143-151, 2023 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 1
  • Basım Tarihi: 2023
  • Dergi Adı: Turkish World Mathematical Society Journal of Applied and Engineering Mathematics
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.143-151
  • Anahtar Kelimeler: Adjoint operator, Dual space, Regularized trace formula., Schatten classes
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

If H is a separable Hilbert space, Gul (2008) has shown that a regularized trace formula can be computed on LL2(H; [0;π ]) for a second order differential operator with bounded operator-valued coeffcients, where H is a separable Hilbert space. Kuelbs (1970) has shown that every separable Banach space can be continuously and densely embedded into a separable Hilbert space, while Gill (2016) has used Kuelbs result to show that the dual of a Banach space does not have a unique representation. In this paper, we use the results of Kuelbs and Gill to study the regularized trace formula on L2(B; [0; π]), where B is an arbitrary separable Banach space