Frechet-Hilbert spaces and the property SCBS


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UYANIK E. , YURDAKUL M. H.

TURKISH JOURNAL OF MATHEMATICS, vol.42, no.3, pp.1294-1297, 2018 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 3
  • Publication Date: 2018
  • Doi Number: 10.3906/mat-1706-58
  • Title of Journal : TURKISH JOURNAL OF MATHEMATICS
  • Page Numbers: pp.1294-1297

Abstract

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.