Article Title

Fréchet-Hilbert spaces and the property SCBS

Authors

ELİF UYANIK
MURAT HAYRETTİN YURDAKUL

DOI

10.3906/mat-1706-58

Abstract

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

Keywords

Locally convex spaces, Fréchet-Hilbert spaces, the SCBS property

First Page

1294

Last Page

1297

Recommended Citation

UYANIK, ELİF and YURDAKUL, MURAT HAYRETTİN (2018) "Fréchet-Hilbert spaces and the property SCBS," Turkish Journal of Mathematics: Vol. 42: No. 3, Article 42. https://doi.org/10.3906/mat-1706-58
Available at: https://journals.tubitak.gov.tr/math/vol42/iss3/42