\(\lambda\)-similar bases (Q1093844)

Let (X,T) and (Y,S) be two Hausdorff locally convex spaces (l.c.s.) with \(D_ T\) and \(D_ S\) as the family of all T- and S-continuous seminorms generating the topologies T and S respectively. For an arbitrarily given sequence space \(\lambda\), a sequence \(\{x_ n\}\) in X is said to be \(\lambda\)-similar to a sequence \(\{y_ n\}\) in Y if for an arbitrary sequence \(\{\alpha_ n\}\) of scalars \(\{\alpha_ np(x_ n)\}\in \lambda\), for all p in \(D_ T\Leftrightarrow \{\alpha_ nq(y_ n)\}\in \lambda\), for all q in \(D_ S.\) This papers contains results which characterize \(\lambda\)-similarity between two Schauder bases and its relationship with \(\lambda\)-bases.