Fréchet-Hilbert spaces and the property SCBS

Authors : Elif UYANIK, Murat Hayrettin YURDAKUL

Pages : 1294-1297

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :In this note, we obtain that all separable Fréchet-Hilbert spaces have the property of smallness up to a complemented Banach subspace insert ignore into journalissuearticles values(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