Symmetric spaces with maximal projection constants
| Autor: | Grzegorz Lewicki, Bruce L. Chalmers |
|---|---|
| Rok vydání: | 2003 |
| Předmět: |
Discrete mathematics
Pure mathematics projection constant Symmetric spaces Maximal overspace Power sum symmetric polynomial Triple system maximal overspace symmetric spaces Stanley symmetric function regular symmetric subspaces Complete homogeneous symmetric polynomial Regular symmetric subspaces Projection constant Symmetric closure Symmetric function Elementary symmetric polynomial Ring of symmetric functions Analysis Mathematics |
| Zdroj: | Journal of Functional Analysis. 200(1):1-22 |
| ISSN: | 0022-1236 |
| DOI: | 10.1016/s0022-1236(02)00080-0 |
| Popis: | In this paper we introduce a special class of finite-dimensional symmetric subspaces of L1, so-called regular symmetric subspaces. Using this notion, we show that for any k⩾2, there exist k-dimensional symmetric subspaces of L1 which have maximal projection constant among all k-dimensional symmetric spaces. Moreover, L1 is a maximal overspace for these spaces (see Theorems 4.4 and 4.5.) Also a new asymptotic lower bound for projection constants of symmetric spaces is obtained (see Theorem 5.3). This result answers the question posed in [12, p. 36] (see also [15, p. 38]) by H. Koenig and co-authors. The above results are presented both in real and complex cases. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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