Topics in ergodic theory: Existence of invariant elements and ergodic decompositions of Banach lattices.

摘要

E is a weakly sequentially complete Banach lattice with a weak unit e. ;One constructs sequences of operator averages, ;The existence of an invariant weak unit is equivalent to the condition that for any nonzero H in ;With further assumption of commutativity on ;The notion of truncated limits is used in the second chapter of results. Let u be a weak unit in E. For a sequence ;In addition to left amenability one assumes either the operators ;It follows that if TL ;Assuming commutativity and passing to Kothe function space representation of E, one obtains the decompositions of the Banach lattice of the form E = Y + Z = P + D + Z, where the 'remaining part' Y is the maximal support of ;A unified proof for the above results is given in a more general setting of an order continuous seminorm N satisfying condition (C) and the following condition: For any sequence