IJPAM: Volume 27, No. 2 (2006)
REAL ANALYTIC ``-NORMS''
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: [email protected]
Abstract.Here we point out the following consequences of a previous result of mine. Let be a Hausdorff and locally convex topological vector space without any continuous norm and an -norm defining the topology of . Then there is no pair with an open neighborhood of and a real analytic function such that and the sets form a fundamental system of open neighborhoods of in . Furthermore, there is no strictly increasing function such that is real analytic.
Received: November 29, 2005
AMS Subject Classification: 32K05, 32D20, 46E99
Key Words and Phrases: real analytic function in infinite-dimensional topological vector space, topological vector space without a continuous norm, real analytic function
Source: International Journal of Pure and Applied Mathematics