2023/02/07 by Alejandro Chávez-Domínguez, Chávez-Domínguez, Alejandro, Verónica Dimant +3
Mathematics · Physics and Astronomy · #46B28 (Primary) 46L06 (Secondary) #46M05 #47L25 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2302.03696
openalex publication_date 2023/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The use of a tensor product perspective has enriched functional analysis and other important areas of mathematics and physics. The context of operator spaces is clearly no exception. The aim of this manuscript is to kick off the development of a systematic theory of tensor products and tensor norms for operator spaces and its interplay with their associated mapping ideals. Based on the theory of tensor products in Banach spaces, we provide the corresponding natural definitions in the operator space framework. The theory is not a mere translation of what is known in the classical setting and new insights, techniques, ideas or hypotheses are required in many cases. As a consequence, notable differences in the theory appear when compared to the classical one.