A remark to a theorem of Yu. A. Abramovich

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Emel'yanov E.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, cilt.132, sa.3, ss.781-782, 2004 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 132 Sayı: 3
  • Basım Tarihi: 2004
  • Doi Numarası: 10.1090/s0002-9939-03-07111-9
  • Dergi Adı: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.781-782
  • Anahtar Kelimeler: positive isometry, doubly power bounded operator, renorming problem
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

A remarkable theorem due to Abramovich (1988) states that any surjective positive isometry on a Banach lattice has a positive inverse. In this note we discuss a renorming problem for Banach lattices and show that the theorem cannot be generalized to the case of the doubly power bounded positive operators.