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Köthe coechelon spaces as locally convex algebras

José Bonet, Paweł Domański (2010)

Studia Mathematica

We study those Köthe coechelon sequence spaces k p ( V ) , 1 ≤ p ≤ ∞ or p = 0, which are locally convex (Riesz) algebras for pointwise multiplication. We characterize in terms of the matrix V = (vₙ)ₙ when an algebra k p ( V ) is unital, locally m-convex, a -algebra, 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...

Köthe spaces modeled on spaces of C functions

Mefharet Kocatepe, Viacheslav Zahariuta (1996)

Studia Mathematica

The isomorphic classification problem for the Köthe models of some C function spaces is considered. By making use of some interpolative neighborhoods which are related to the linear topological invariant D φ and other invariants related to the “quantity” characteristics of the space, a necessary condition for the isomorphism of two such spaces is proved. As applications, it is shown that some pairs of spaces which have the same interpolation property D φ are not isomorphic.

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