Problems in matricially derived solid Banach sequence spaces

Let F N denote the vector space of all scalar sequences. If A is an innite matrix with nonnegative entries and is a solid subspace of F N , then sol A 1 ( ) = f x 2 F N : Aj xj 2 g is also a solid subspace of F N that, under certain conditions on A and , inherits a solid topological vector space topology from any such topology on . Letting 0 = and m = sol A 1 ( m 1) for m > 0, we derive an innite sequence 0; 1; 2;::: of solid subspaces of F N from the inputs A and . For A and conned to certain classes, we ask many questions about this derived sequence and answer a few.