A closedness theorem for normed spaces

• Autorzy: Poppe H.
• Języki publikacji: EN

Abstrakty

EN

For spaces X, Y, for which some algebraic operations are defined and in some cases topologies for X, Y are defined too, we define for the space X a dual space Xd with respect to the space Y. If [..] is a topology for Y (compatible with the algebraic operations of Y), then the pointwise topology rp for Yx is defined. We show that Xd is (algebraically)rp-closed in Yx. For normed spaces is shown that suitable subspaces of Xd are rp-closed in a product space K C Yx. As a corollary we obtain a generalization of Alaoglu's theorem.

Słowa kluczowe

EN

generalized dual space; rings; pointwise topology; normed space; Alaoglu's theorem

PL

pierścienie; topologia punktowa; przestrzeń unormowana; twierdzenie Alaoglu'sa

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2008
• Tom: Vol. 41, nr 1
• Strony: 123--127
• Opis fizyczny: Bibliogr. 1 poz.

Twórcy

autor

Poppe H.

• Institute of Mathematics University of Rostock, Universitatsplatz 1 18051 Rostock, Germany,

Bibliografia

• [1] J. B. Conway, A Course in Functional Analysis, Second Edition, New York, Springer 1990.