Some remarks on Orlicz's interpolation theorem
Some results are presented, concerning a class of Banach spaces introduced by G. Godefroy and M. Talagrand, the representable Banach spaces. The main aspects considered here are the stability in forming tensor products, and the topological properties of the weak* dual unitball.
Para un b-espacio nuclear N y un b-espacio E demostramos que si X es un espacio compacto entonces los b-espacios C (X,NεE) y NεC (X,E) son isomorfos. El mismo resultado se verifica también si X es un espacio localmente compacto que es numerable en el infinito.
In this paper we suggest a general framework of the spectral mapping theorem in terms of parametrized Banach space bicomplexes.
We revisit the old result that biflat Banach algebras have the same cyclic cohomology as C, and obtain a quantitative variant (which is needed in separate, joint work of the author on the simplicial and cyclic cohomology of band semigroup algebras). Our approach does not rely on the Connes-Tsygan exact sequence, but is motivated strongly by its construction as found in [2] and [5].
Soit la -algèbre, ou bien réduite ou bien maximale, associée à la variété feuilletée , et la -algèbre élémentaire des opérateurs compacts. Alors, si dim, on montre que est isomorphe à .
We introduce an algebraic notion-stability-for an element of a commutative ring. It is shown that the stable elements of Banach algebras, and of Fréchet algebras, may be simply described. Part of the theory of power-series embeddings, given in [1] and [4], is seen to be of a purely algebraic nature. This approach leads to other natural questions.