A free convenient vector space for holomorphic spaces |
| |
Authors: | E Siegl |
| |
Institution: | (1) Department of Mathematics and Statistics, Carleton University, K1S 5B6 Ottawa, Ontario, Canada |
| |
Abstract: | In this paper we show that there exists a free convenient vector space for the case of holomorphic spaces and holomorphic maps. This means that for every spaceX with a holomorphic structure, there exists an appropriately complete locally convex vector space X and a holomorphic mapl
X:X![rarr](/content/v8g632205h786w28/xxlarge8594.gif) X, such that for any vector space of the same kind the map (l
X
)*:L( X,E)![rarr](/content/v8g632205h786w28/xxlarge8594.gif) (X,E) is a bijection. Analogously to the smooth case treated in 2, 5.1.1] the free convenient vector space X can be obtained as the Mackey closure of the linear subspace spanned by the image of the canonical mapX![rarr](/content/v8g632205h786w28/xxlarge8594.gif) (X ) .In the second part of the paper we prove that in the case whereX is a Riemann surface, one has X= (X, ) . |
| |
Keywords: | Primary 46G20 Secondary 58B12 58C10 |
本文献已被 SpringerLink 等数据库收录! |
|