Mean ergodicity of positive operators in <i>KB</i>-space

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Alpay S., Binhadjah A., Emelyanov E. Y., Ercan Z. M.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, cilt.323, sa.1, ss.371-378, 2006 (SCI-Expanded, Scopus)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 323 Sayı: 1
• Basım Tarihi: 2006
• Doi Numarası: 10.1016/j.jmaa.2005.10.054
• Dergi Adı: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Sayfa Sayıları: ss.371-378
• Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

We prove that any positive power bounded operator T in a KB-space E which satisfies [GRAPHICS] where BE is the unit ball of E, g epsilon E+, and 0 <= eta < 1, is mean ergodic and its fixed space Fix(T) is finite dimensional. This generalizes the main result of [E.Yu. Emelyanov, M.P.H. Wolff, Mean lower bounds for Markov operators, Ann. Polon. Math. 83 (2004) 11-19]. Moreover, under the assumption that E is a sigma-Dedekind complete Banach lattice, we prove that if, for any positive power bounded operator T, the condition (1) implies that T is mean ergodic then E is a KB-space. (c) 2005 Elsevier Inc. All rights reserved.