Absolutely Summing Processes

Abstract

Absolutely summing processes are defined, which form a subclass of weakly operator harmonizable processes. When the parameter space is the set of real numbers, it is proved that an absolutely summing process is represented as an integral of operator stationary processes with respect to an appropriate probability measure. To do this, weak convergence of scalar and vector measures is considered. Then we prove compactness of the unit ball of vector measures under certain topologies, and we apply the Choquet theorem to derive an integral representation.

Keywords:

• Absolutely summing operators
• Absolutely summing processes
• Choquet type theorem
• Pointwise weak* topology
• Pointwise weak topology
• Weak topology

Mathematics Subject Classification:

• Primary 60G12
• Secondary 28B05
• 47B10