  In order to measure qualitative properties we introduce a notion of a type
for arbitrary normed spaces which measures the worst possible growth of partial
sums of sequences weakly converging to zero. The ideas can be traced back to
Banach and Mazur who used this type to compare the so-called linear dimension
of classical Banach spaces. As an application we compare the linear dimension
and investigate isomorphy of some classical Banach spaces.
