The strongest vector space topology is locally convex on separable linear subspaces

• Autorzy: W. Żelazko
• Języki publikacji: EN

Abstrakty

EN

Let X be a real or complex vector space equipped with the strongest vector space topology $τ_{max}$. Besides the result announced in the title we prove that X is uncountable-dimensional if and only if it is not locally pseudoconvex.

Słowa kluczowe

EN

topological vector spaces   locally pseudoconvex spaces   locally convex subspaces  

Kategorie tematyczne

• 46A16: Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1997
• Tom: 66
• Numer: 1
• Strony: 275-282

Daty

wydano

1997

otrzymano

1995-04-26

Twórcy

autor

W. Żelazko

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, P.O. Box 137, 00-950 Warszawa, Poland

Bibliografia

• [1] S. Banach, Théorie des Opérations Linéaires, Warszawa, 1932.
• [2] N. Dunford and J. T. Schwartz, Linear Operators I, Interscience, New York, 1958.
• [3] H. Jarchow, Locally Convex Spaces, Teubner, Stuttgart, 1981.
• [4] A. Grothendieck, Topological Vector Spaces, Gordon and Breach, New York, 1973.
• [5] A. Kokk and W. Żelazko, On vector spaces and algebras with maximal locally pseudoconvex topologies, Studia Math. 112 (1995), 195-201.
• [6] G. Köthe, Topological Vector Spaces I, Springer, Berlin, 1969.
• [7] G. Köthe, Topological Vector Spaces II, Springer, Berlin, 1979.
• [8] S. Rolewicz, Metric Linear Spaces, PWN, Warszawa, 1972.
• [9] H. H. Schaefer, Topological Vector Spaces, Springer, New York, 1971.
• [10] L. Waelbroeck, Topological Vector Spaces and Algebras, Lecture Notes in Math. 230, Springer, 1971.
• [11] A. Wilansky, Modern Methods in Topological Vector Spaces, McGraw-Hill, New York, 1978.