Shrinking Schauder Basis for a Banach Space

Question

Let $E$ be a Banach space with a Schauder basis. Let $S_n$ be the operator of partial sum. We say that the Schauder basis is shrinking if for every $f \in E^*$ we have $f○S_n \rightarrow f$ in the norm topology of $E^*$ .

Where can such definition be found ?

Answer 1

You will find it in

Ivan Singer: Bases in Banach Spaces I (Springer)

Chapter II, § 4: k - shrinking bases.