scholarly journals Dixmier measurability in Marcinkiewicz spaces and applications

2013 ◽  
Vol 265 (12) ◽  
pp. 3053-3066 ◽  
Author(s):  
A.A. Sedaev ◽  
F.A. Sukochev
Keyword(s):  
Marcinkiewicz Spaces

scholarly journals Banach–Saks property in Marcinkiewicz spaces

2007 ◽  
Vol 336 (2) ◽  
pp. 1231-1258 ◽  
Author(s):  
S.V. Astashkin ◽  
F.A. Sukochev
Keyword(s):  
Marcinkiewicz Spaces

scholarly journals Noncommutative weighted individual ergodic theorems with continuous time

2020 ◽  
Vol 23 (02) ◽  
pp. 2050013
Author(s):  
Vladimir Chilin ◽  
Semyon Litvinov
Keyword(s):  
Ergodic Theorem ◽  
Continuous Time ◽  
Symmetric Spaces ◽  
Von Neumann Algebra ◽  
Ergodic Theorems ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Von Neumann ◽  
Marcinkiewicz Spaces ◽  
Local Ergodic Theorem

We show that ergodic flows in the noncommutative [Formula: see text]-space (associated with a semifinite von Neumann algebra) generated by continuous semigroups of positive Dunford–Schwartz operators and modulated by bounded Besicovitch almost periodic functions converge almost uniformly. The corresponding local ergodic theorem is also proved. We then extend these results to arbitrary noncommutative fully symmetric spaces and present applications to noncommutative Orlicz (in particular, noncommutative [Formula: see text]-spaces), Lorentz, and Marcinkiewicz spaces. The commutative counterparts of the results are derived.

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