Fréchet-Hilbert spaces and the property SCBS | Zendy

Elif Uyanık | Zendy; Murat Yurdakul | Zendy

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Fréchet-Hilbert spaces and the property SCBS

Author(s) -

Elif Uyanık,

Murat Yurdakul

Publication year - 2018

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1706-58

Subject(s) - mathematics , banach space , hilbert space , separable space , bounded function , subspace topology , pure mathematics , hilbert manifold , banach manifold , fréchet space , automorphism , property (philosophy) , bounded operator , rigged hilbert space , perturbation (astronomy) , mathematical analysis , lp space , interpolation space , functional analysis , unitary operator , biochemistry , chemistry , philosophy , physics , epistemology , quantum mechanics , gene

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.

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