The α σ -Approximation Property and Its Related Operator Ideals

Ju Myung Kim ()
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Ju Myung Kim: Department of Mathematics and Statistics, Sejong University, Seoul 05006, Republic of Korea

Mathematics, 2024, vol. 12, issue 13, 1-9

Abstract: In this paper, we study the σ -tensor norm ( α σ ), the absolutely τ -summing operator and the σ -nuclear operator. We characterize the α σ -approximation property in terms of some density of the space of absolutely τ -summing operators. When X * or Y * * * has the approximation property, we prove that an operator T from X to Y is σ -nuclear if the adjoint of T is σ -nuclear.

Keywords: tensor norm; approximation property; operator ideal (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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