Asymptotically symmetric spaces with hereditarily non-unique spreading models
Copyright policy )Asymptotically symmetric spaces with hereditarily non-unique spreading models
We examine a variant of a Banach space $\mathfrak{X}_{0,1}$ defined by Argyros, Beanland, and the second named author that has the property that it admits precisely two spreading models in every infinite dimensional subspace. We prove that this space is asymptotically symmetric and thus it provides a negative answer to a problem of Junge, the first. named author, and Odell.
12 pages
- University of Illinois at Urbana Champaign United States
- University of Illinois at Urbana–Champaign United States
Mathematics - Functional Analysis, Isomorphic theory (including renorming) of Banach spaces, 46B03, 46B06, 46B25, 46B45, Asymptotic theory of Banach spaces, FOS: Mathematics, asymptotically symmetric space, spreading model, Classical Banach spaces in the general theory, Banach sequence spaces, Functional Analysis (math.FA)
Mathematics - Functional Analysis, Isomorphic theory (including renorming) of Banach spaces, 46B03, 46B06, 46B25, 46B45, Asymptotic theory of Banach spaces, FOS: Mathematics, asymptotically symmetric space, spreading model, Classical Banach spaces in the general theory, Banach sequence spaces, Functional Analysis (math.FA)
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