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Frechet-Hilbert spaces and the property SCBS
Date
2018-01-01
Author
Uyanik, Elif
Yurdakul, Murat Hayrettin
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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.
Subject Keywords
Locally convex spaces
,
Frechet-Hilbert spaces
,
The SCBS property
URI
https://hdl.handle.net/11511/31606
Journal
TURKISH JOURNAL OF MATHEMATICS
DOI
https://doi.org/10.3906/mat-1706-58
Collections
Graduate School of Natural and Applied Sciences, Article
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E. Uyanik and M. H. Yurdakul, “Frechet-Hilbert spaces and the property SCBS,”
TURKISH JOURNAL OF MATHEMATICS
, pp. 1294–1297, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/31606.