We give a representation of the spaces C∞(RN)∩Hk,p(RN) as spaces of vector-valued sequences and use it to investigate their topological properties and isomorphic classification. In particular, it is proved that C∞(RN)∩Hk,2(RN) is isomorphic to the sequence space sNℓ2(ℓ2), thereby showing that the isomorphy class does not depend on the dimension N if p=2
In this paper we study the complemented subspaces of the spaces (lp)N∩lq(lq), with 1≤p<q≤∞ or q=0, thereby showing that if (\l^p)^\N\cap l^q(l^q)=F\oplus G then either F or G contains a complemented copy of the whole space
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