Frechet-Hilbert spaces and the property SCBS


Uyanik E., YURDAKUL M. H.

TURKISH JOURNAL OF MATHEMATICS, cilt.42, ss.1294-1297, 2018 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 42 Konu: 3
  • Basım Tarihi: 2018
  • Doi Numarası: 10.3906/mat-1706-58
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Sayfa Sayıları: ss.1294-1297

Özet

In this note, we obtain that all separable Frechet-Hilbert spaces have the property of smallness up to a complemented Banach subspace (SCBS). Djakov, Terzioglu, Yurdakul, and Zahariuta proved that a bounded perturbation of an automorphism on Frechet spaces with the SCBS property is stable up to a complemented Banach subspace. Considering Frechet-Hilbert spaces we show that the bounded perturbation of an automorphism on a separable Frechet-Hilbert space still takes place up to a complemented Hilbert subspace. Moreover, the strong dual of a real Frechet-Hilbert space has the SCBS property.