Charakterisierung der Quotientenräume von s und eine Vermutung von Martineau
We investigate conditions under which the projective and the injective topologies coincide on the tensor product of two Köthe echelon or coechelon spaces. A major tool in the proof is the characterization of the επ-continuity of the tensor product of two diagonal operators from to . Several sharp forms of this result are also included.
The following result is proved: Let E be a complemented subspace with an r-finite-dimensional decomposition of a nuclear Köthe space λ(A). Then E has a basis.
New compound geometric invariants are constructed in order to characterize complemented embeddings of Cartesian products of power series spaces. Bessaga's conjecture is proved for the same class of spaces.