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Further properties of Azimi-Hagler banach spaces

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Abstract

For the Azimi-Hagler spaces more geometric and topological properties are investigated. Any constructed space is denoted by X α,p . We show

  1. (i)

    The subspace [(e nk )] generated by a subsequence (e nk ) of (e n ) is complemented.

  2. (ii)

    The identity operator from X α,p to X α,p when p > q is unbounded.

  3. (iii)

    Every bounded linear operator on some subspace of X α,p is compact. It is known that if any X α,p is a dual space, then

  4. (iv)

    duals of X α,1 spaces contain isometric copies of ℓ ∞ and their preduals contain asymptotically isometric copies of c 0.

  5. (v)

    We investigate the properties of the operators from X α,p spaces to their predual.

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Authors and Affiliations

  1. Payame Noor University, Dargaz, Iran

    H. Khodabakhshian

Authors
  1. Parviz Azimi
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  2. H. Khodabakhshian
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Correspondence to H. Khodabakhshian.

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Azimi, P., Khodabakhshian, H. Further properties of Azimi-Hagler banach spaces. Czech Math J 59, 871–878 (2009). https://doi.org/10.1007/s10587-009-0061-z

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  • DOI: https://doi.org/10.1007/s10587-009-0061-z

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