Some open questions on positive operators in Banach lattices
Journal: Владикавказский математический журнал @vmj-ru
Article in issue: 4 т.7, 2005.
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Recently, some new results on asymptotic behaviour of positive operators in Banach lattices were obtained. Here we discuss some open problems related to these results.
Similar articles in the section Analysis
Short address: https://sciup.org/14318163
IDS: 14318163 | UDC: 517.98
References Some open questions on positive operators in Banach lattices
- Abramovich Yu. A. Isometries of normed lattices//Optimizatsiya.-1988.-V. 43 (60).-P. 74-80.
- Abramovich Yu. A., Aliprantis C. D. An invitation to operator theory//Graduate Studies in Mathematics, V. 50.-2002, Providence, RI: American Mathematical Society.-xiv+530 p.
- Alpay S., Binhadjah A., Emel'yanov E. Yu. A Positive Doubly Power Bounded Operator on an AL-Space with a Nonpositive Inverse. [Preprint]
- Derriennic Y., Krengel U. Subadditive mean ergodic theorems//Ergodic Theory Dynamical Systems.-1981.-V. 1, № 1.-P. 33-48.
- Eisner T. Privat communication.
- Emel'yanov E. Yu. Banach lattices on which every power-bounded operator is mean ergodic//Positivity.-1997.-V. 1, № 4.-P. 291-296.
- Emel'yanov E. Yu. A remark to a theorem of Yu. A. Abramovich//Proc. Amer. Math. Soc.-2004.-V. 132, № 3.-P. 781-782.
- Emel'yanov E. Yu., Wolff M. P. H. Mean ergodicity on Banach lattices and Banach spaces//Arch. Math. (Basel).-1999.-V. 72, № 3.-P. 214-218.
- Fonf V. P., Lin M., Wojtaszczyk P. Ergodic Characterization of Reflexivity of Banach spaces//J. Funct. Anal.-2001.-V. 187.-P. 146-162.
- Huijsmans C. B. Lattice-ordered division algebras//Proc. Roy. Irish Acad. Sect.-1992.-V. A 92, № 2.-P. 239-241.
- Komornik J. Asymptotic periodicity of Markov and related operators//Dynamics reported, Dynam. Report. Expositions Dynam. Systems (N.S.).-Berlin: Springer, 1993.-V. 2.-P. 31-68.
- Kornfeld I., Lin M. Weak almost periodicity of L\sb 1-contractions and coboundaries of non-singular transformations//Studia Math.-2000.-V. 138, № 3.-P. 225-240.
- Krengel U. Ergodic Theorems.-Berlin-New York: De Gruyter, 1985.
- Lyubich Yu. I. Introduction to the Theory of Banach Representations of Groups.-Basel, Boston, Berlin: Birkhauser, 1988.
- Meyer-Nieberg P. Banach Lattices//Universitext.-Berlin: Springer-Verlag, 1991.
- Rabiger F. Ergodic Banach lattices//Indag. Math. (N.S.).-1990.-V. 1, № 4.-P. 483-488.
- Schaefer H. H., Wolff M. P. H., Arendt W. On lattice isomorphisms with positive real spectrum and groups of positive operators//Math. Z.-1978.-V. 164, № 2.-P. 115-123.
- Sine R. A mean ergodic theorem//Proc. Amer. Math. Soc.-1970.-V. 24, № 2.-P. 438-439.
- Sine R. A note on the ergodic properties of homeomorphisms//Proc. Amer. Math. Soc.-1976.-V. 57, № 1.-169-172.
- Sucheston L. Open questions, probability in Banach spaces//Oberwolfach.-Berlin-Heidelberg-New York: Springer, 1975.-P. 285-289. (Lecture Notes in Math.-1976.-№ 526.)
- Zaharopol R. Mean ergodicity of power-bounded operators in countably order complete Banach lattices//Math. Z.-1986.-V. 192, № 1.-P. 81-88.
