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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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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.

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Eugene Tokarev. 2002-10-25. An example of a Banach Space with a Subsymmetric Basis, which has the Hereditarily Approximation Property. https://arxiv.org/abs/math/0206108

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