Abstract. Sufficient conditions are given on a Banach space X which ensure that `∞ embeds in L (X), the space of all bounded linear operators on X. A basic sequence (en) is said to be quasisubsymmetric if for any two increasing sequences (kn) and (`n) of positive integers with kn ≤ `n for all n, (ekn) dominates (e`n). If a Banach space X has a seminormalized quasisubsymmetric basis then `∞ embe...

The diverse array of protein functions depends upon these molecules’ reliable ability to fold into the native structures determined by their amino-acid sequences. Because mutations that alter a protein’s sequence frequently disrupt its folding, protein evolution explores protein sequence space conservatively, either by point mutations or recombination between related sequences. Attempts to engi...

We obtain the expression of Ricci tensor for a $GCR$-lightlikesubmanifold of indefinite complex space form and discuss itsproperties on a totally geodesic $GCR$-lightlike submanifold of anindefinite complex space form. Moreover, we have proved that everyproper totally umbilical $GCR$-lightlike submanifold of anindefinite Kaehler manifold is a totally geodesic $GCR$-lightlikesubmanifold.