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Mean Ergodic Theorems in Jordan Banach Weak Algebras



Author(s)

Panagiotis N. Koumantos1 and Panaiotis K. Pavlakos2

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DOI:10.17265/2159-5291/2013.03.006

1. Department of Mathematics and Department of Physics, National and Kapodistrian University of Athens, Athens, Panepistimiopolis GR-15784, Greece
2. Department of Mathematics, National and Kapodistrian University of Athens, Athens, Panepistimiopolis GR-15784, Greece

The purpose of this paper is to study mean ergodic theorems concerning continuous or positive operators taking values in Jordan-Banach weak algebras and Jordan C*-algebras, making use the topological and order structures of the corresponding spaces. The results are obtained applying or extending previous classical results and methods of Ayupov, Carathéodory, Cohen, Eberlein, Kakutani and Yosida. Moreover, this results can be applied to continious or positive operators appearing in diffusion theory, quantum mechanics and quantum probability theory.

Jordan Banach weak algebras, Krein spaces, mean ergodic operators.