Metrizable weak barrelledness and dimension

• Autorzy: Saxon S. , Sanchez Ruiz L.
• Języki publikacji: EN

Abstrakty

EN

The least infinite-dimensionality for Frechet spaces is c (Mazur), for metrizable barrelled spaces, b (Saxon and Sanchez Ruiz, 1996). For metrizable spaces with the yet weaker inductive property, it is the dimension Aleph[1] of the space chi spanned by any Aleph[1] scalar sequences of the form [(1, x, x^2, x^3, . . .)]. (A locally convex space is inductive if it is the inductive limit of each increasing covering sequence of subspaces). Indeed, chi is a non-barrelled subspace of the Frechet space omega, where the fundamental theorem of algebra at once proves density, dimension and inductivity. Moreover, if each |x| < 1, geometric series then put chi inside the Banach space [l^1], where the identity principle similarly proves the normable case.

Słowa kluczowe

EN

c[0] and [l^p]; fundamental theorem of algebra; geometric and power series; inductive and primitive spaces; least infinite-dimensionality; metrizable; omega; S[sigma]

PL

przestrzeń indukcyjna i pierwotna; przestrzeń metryzowalna; szereg geometryczny i potęgowy; zasadnicze twierdzenie algebry

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2001
• Tom: Vol. 49, no 2
• Strony: 97--101
• Opis fizyczny: Bibliogr. 15 poz.,

Twórcy

autor

Saxon S.

autor

Sanchez Ruiz L.