Lecture Notes in Mathematics

This book provides a comprehensive introduction to the systematic theory of tensor products and tensor norms within the framework of operator spaces. The use of tensor products has significantly advanced functional analysis and other areas of mathematics and physics, and the field of operator spaces is no exception. Building on the theory of tensor products in Banach spaces, this work adapts the definitions and results to the operator space context. This approach goes beyond a mere translation of existing results. It introduces new insights, techniques, and hypotheses to address the many challenges of the non-commutative setting, revealing several notable differences to the classical theory. This text is expected to be a valuable resource for researchers and advanced students in functional analysis, operator theory, and related fields, offering new perspectives for both the mathematics and physics communities. By presenting several open problems, it also serves as a potential source for further research, particularly for those working in operator spaces or operator algebras.