Frechet-Hilbert spaces and the property SCBS

2018-01-01
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.
Citation Formats
E. Uyanik and M. H. Yurdakul, “Frechet-Hilbert spaces and the property SCBS,” pp. 1294–1297, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/31606.