Köthe coechelon spaces as locally convex algebras

We study those Kothe co-echelon sequence spaces kp(V ), 1 ≤ p ≤ ∞ or p = 0, which are locally convex (Riesz) algebras for the pointwise multiplication. We characterize in terms of the matrix V = (vn)n when an algebra kp(V ) is unital, locally m-convex, a Q-algebra, it has a continuous (quasi)-inverse, all entire functions act on it or some transcendental entire functions act on it. It is proved that all multiplicative functionals are continuous and a precise description of all regular and all degenerate maximal ideals is given even for arbitrary solid algebras of sequences with pointwise multiplication. In particular, it is shown that all regular maximal ideals are solid. 2010 Mathematics Subject Classification: Primary 46H05; Secondary 46A04, 46A45, 46A13, 46J05.