Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1706-58
Keywords
Locally convex spaces, Fréchet-Hilbert spaces, the SCBS property
First Page
1294
Last Page
1297
Recommended Citation
UYANIK, E, & YURDAKUL, M. H (2018). Fréchet-Hilbert spaces and the property SCBS. Turkish Journal of Mathematics 42 (3): 1294-1297. https://doi.org/10.3906/mat-1706-58
