Finite representability of l(p) in quotients of Banach spaces

A typical result of the paper states that if X is a Banach space with a bas is and for some 1 less than or equal top less than or equal toq less than o r equal to infinity, the spaces l(p) and l(q) are finitely block representa ble in every block subspace of X, then every block subspace of X admits a b lock quotient Z such that for every r is an element of [p,q], the space l(r ) is finitely block representable in Z. Results of a similar nature are als o established for l(p)(N)-block-sequences and asymptotic spaces.