Operator Ideals arising from Generating Sequences
Ngai-Ching Wong
TL;DR
This paper explores how operator ideals on Banach spaces are connected to the sequential structures they induce, providing concrete examples involving various classes of compact and Banach-Saks operators.
Contribution
It establishes relationships between operator ideals and their associated sequential structures, with specific examples of classical operator classes.
Findings
Connections between operator ideals and sequential structures
Examples of compact and Banach-Saks operator classes
Insights into the structure of operator ideals on Banach spaces
Abstract
In this note, we will discuss how to relate an operator ideal on Banach spaces to the sequential structures it defines. Concrete examples of ideals of compact, weakly compact, completely continuous, Banach-Saks and weakly Banach-Saks operators will be demonstrated.
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