scholarly journals On the Ergodic Theorem for Affine Actions on Hilbert Space

2015 ◽  
Vol 22 (3) ◽  
pp. 429-446
Author(s):  
Ionut Chifan ◽  
Thomas Sinclair
Keyword(s):  
Hilbert Space ◽  
Ergodic Theorem ◽  
Affine Actions

Fixed Point Theorem and Nonlinear Ergodic Theorem for Nonexpansive Semigroups Without Convexity

1992 ◽  
Vol 44 (4) ◽  
pp. 880-887 ◽  
Author(s):  
Wataru Takahashi
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Ergodic Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Nonexpansive Semigroups ◽  
Amenable Semigroups ◽  
Nonlinear Ergodic Theorem

AbstractWe first prove a nonlinear ergodic theorem for nonexpansive semigroups without convexity in a Hilbert space. Further we prove a fixed point theorem for non-expansive semigroups without convexity which generalizes simultaneously fixed point theorems for left amenable semigroups and left reversible semigroups.

scholarly journals ON THE ENTANGLED ERGODIC THEOREM

2007 ◽  
Vol 10 (01) ◽  
pp. 67-77 ◽  
Author(s):  
FRANCESCO FIDALEO
Keyword(s):  
Hilbert Space ◽  
Ergodic Theorem ◽  
Unitary Operator ◽  
Compact Operators ◽  
Ergodic Average ◽  
Periodic Case ◽  
Almost Periodic ◽  
Ergodic Averages ◽  
Weak Operator Topology ◽  
Weak Operator

Let U be a unitary operator acting on the Hilbert space [Formula: see text], and α: {1, …, m} ↦ {1, …, k} a partition of the set {1, …, m}. We show that the ergodic average [Formula: see text] converges in the weak operator topology if the Aj belong to the algebra of all the compact operators on [Formula: see text]. We write esplicitly the formula for these ergodic averages in the case of pair-partitions. Some results without any restriction on the operators Aj are also presented in the almost periodic case.

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