<?xml version="1.0" encoding="utf-8"?>
<journal>
  <journal_metadata lang="en">
    <full_title>Bulletin of the Australian Mathematical
    Society</full_title>
    <abbrev_title>Bull. Austral. Math. Soc.</abbrev_title>
    <issn media_type="online">0004-9727</issn>
    <coden>ALNBAB</coden>
  </journal_metadata>
  <journal_issue>
    <publication_date media_type="online">
      <year>2005</year>
    </publication_date>
    <journal_volume>
      <volume>72</volume>
    </journal_volume>
    <issue>1</issue>
    <doi_data>
      <doi>10.wxyz/CV72P1</doi>
      <resource>
      http://www.austms.org.au/Publ/Bulletin/V72P1/</resource>
    </doi_data>
  </journal_issue>
  <journal_article publication_type="full_text">
    <titles>
      <title>A nonlinear map for midpoint locally uniformly rotund
      renorming</title>
    </titles>
    <contributors>
      <person_name sequence="first" contributor_role="author">S.
      Lajara</person_name>
      <person_name sequence="additional" contributor_role="author">
      A.J. Pallarés</person_name>
    </contributors>
    <publication_date media_type="online">
      <given_date>14 February 2006</given_date>
      <year>2006</year>
      <month>2</month>
      <day>14</day>
    </publication_date>
    <pages>
      <first_page>39</first_page>
      <last_page>44</last_page>
    </pages>
    <publisher_item>
      <item_number>721-5030-LaPa-2005</item_number>
    </publisher_item>
    <doi_data>
      <doi>10.wxyz/C2005V72P1p39</doi>
      <resource>
      http://www.austms.org.au/Publ/Bulletin/V72P1/721-5030-LaPa/</resource>
    </doi_data>
    <extra_info>
      <abstract>We provide a criterion for midpoint locally
      uniformly rotund renormability of normed spaces involving the
      class of $\sigma $-slicely continuous maps, recently
      introduced by Molt\'o, Orihuela, Troyanski and Valdiva in
      2003. As a consequence of this result, we obtain a theorem of
      G. Alexandrov concerning the three space problem for midpoint
      locally uniformly rotund renormings of Banach
      spaces.</abstract>
      <subject_class>46B20, 54E99,54H05</subject_class>
      <review type="MathReviews">MR2162292</review>
      <review type="Zentralblatt">02212184</review>
      <acknowledgement>Research supported by MCYT BFM 2002-01719
      and CARM Séneca 00690-PI-04</acknowledgement>
    </extra_info>
    <citation_list>
      <citation>
        <structured_citation>
          <author>G. Alexandrov</author>
          <title type="article">On the three space problem for MLUR
          renorming of Banach spaces</title>
          <medium type="journal" volume="42" year="1989"
          pages="17--20">C. R. Acad. Bulgare Sci.</medium>
          <MRnumber>MR1049438</MRnumber>
        </structured_citation>
        <unstructured_citation style="LaTeX">G. Alexandrov; On the
        three space problem for MLUR renorming of Banach spaces,
        \textit{C. R. Acad. Bulgare Sci.} \textbf{42} (1989),
        pp.~17--20.</unstructured_citation>
      </citation>
      <citation>
        <structured_citation>
          <author>G. Alexandrov and I. Dimitrov</author>
          <title type="article" status="in book">On equivalent
          weakly midpoint locally uniformly rotund renormings of
          the space 
          <span class="MATH">
            <i>ℓ {∞ }</i>
          </span></title>
          <extra_info type="paper">(in Russian)</extra_info>
          <medium type="book" year="1985" pages="189--191">Math.
          and Math. Education</medium>
          <extra_info type="series">Proc. 14th Spring Conference of
          the Union of Bulg. Mathematicians, Sunny
          Beach</extra_info>
          <publisher address="Sofia">Blgar. Akad. Nauk</publisher>
        </structured_citation>
        <unstructured_citation style="LaTeX">G. Alexandrov and I.
        Dimitrov; On equivalent weakly midpoint locally uniformly
        rotund renormings of the space $\ell {\infty }$, (in
        Russian), in \textit{Math. and Math. Education}, Proc. 14th
        Spring Conference of the Union of Bulg. Mathematicians,
        Sunny Beach (Blgar. Akad. Nauk, Sofia, 1985),
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          <author>R. Deville, G. Godefroy and V. Zizler</author>
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          <publisher address="Harlow">Longman Scientific and
          Technical</publisher>
          <MRnumber>MR1211634</MRnumber>
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          <author>G. Godefroy, S. Troyanski, J. Whitfield and V.
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        for locally uniformly rotund renormings of Banach spaces,
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        renorming theory, \textit{Proc. London Math. Soc.}
        \textbf{78} (1999), pp.~541--585.</unstructured_citation>
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          <author>Z. Hu, W.B. Moors and M.A. Smith</author>
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          <author>M. Jiménez Sevilla and J.P. Moreno</author>
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        and J.P. Moreno; Renorming Banach spaces with the Mazur
        Intersection Property, \textit{J. Funct. Anal.}
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          <author>K. Kunen and H. Rosenthal</author>
          <title type="article">Martingale proofs of some
          geometrical results in Banach space theory</title>
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        Rosenthal; Martingale proofs of some geometrical results in
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      <citation>
        <structured_citation>
          <author>A. Moltó, J. Orihuela and S. Troyanski</author>
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          and fragmentability</title>
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        <unstructured_citation style="LaTeX">A. Molt\'o, J.
        Orihuela and S. Troyanski; Locally uniformly rotund
        renorming and fragmentability, \textit{Proc. London Math.
        Soc.} \textbf{75} (1997),
        pp.~619--640.</unstructured_citation>
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      <citation>
        <structured_citation>
          <author>A. Moltó, J. Orihuela, S. Troyanski and M.
          Valdivia</author>
          <title type="article">Midpoint locally uniform rotundity
          and a decomposition method for renorming</title>
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        </structured_citation>
        <unstructured_citation style="LaTeX">A. Molt\'o, J.
        Orihuela, S. Troyanski and M. Valdivia; Midpoint locally
        uniform rotundity and a decomposition method for renorming,
        \textit{Q. J. Math.} \textbf{52} (2001),
        pp.~181--193.</unstructured_citation>
      </citation>
      <citation>
        <structured_citation>
          <author>A. Moltó, J. Orihuela, S. Troyanski and M.
          Valdivia</author>
          <title type="article">A non linear transfer
          technique</title>
          <extra_info type="paper">(Prepublicaciones del
          Departamento de Matemáticas de la Universidad de Murcia
          no. 20, 2003)</extra_info>
          <MRnumber>MR1838362</MRnumber>
        </structured_citation>
        <unstructured_citation style="LaTeX">A. Molt\'o, J.
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        uniformly rotund norms, \textit{Mathematika} \textbf{46}
        (1999), pp.~343--358.</unstructured_citation>
      </citation>
    </citation_list>
  </journal_article>
</journal>
