Some open questions on positive operators in Banach lattices
Author: Emelyanov Eduard Yu.
Journal: Владикавказский математический журнал @vmj-ru
Article in issue: 4 т.7, 2005.
Free access
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.
Short address: https://sciup.org/14318163
IDR: 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.
