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An example of a Banach Space with a Subsymmetric Basis, which has the Hereditarily Approximation Property | | Eugene Tokarev
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11 Jun 2002 | | Subject: | Functional Analysis MSC-class: 46B28 (Primary) 46B07, 46B08, 46B20, 46B45 (Secondary) | math.FA | | Abstract: | W.B. Johnson has constructed a series of Banach spaces non isomorphic to the Hilbert one that have the hereditarily approximation property (shortly hereditarily AP): all their subspaces also have the AP. All these examples were ’’sufficiently’’ non-symmetric and this fact allows Johnson to ask: whether there exists any Banach space $X$ with symmetric (or, at least, subsymmetric) basis, distinct from the Hilbert space such that each its subspace has the AP? In this paper is shown that there is a Banach space with a subsymmetric basis (non-equivalent to any symmetric one), which enjoys the hereditarily AP. | | Source: | arXiv, math.FA/0206108 | | Services: | Forum | Review | PDF | Favorites | |
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