Quotients of quantum bornological spaces
The duality theory for operator spaces consists of two main results. One is that for an operator space \(X \subset V\), the restriction \(\phi: V^* \to X^*\) defined by \(\phi(f)=f|_X\) is an exact matrix quotient mapping. The other is that any complete operator space is a matrix quotient of an \(L^1\)-direct sum of finite-dimensional trace class algebras up to a matrix isometry. These properties play key roles in tensor products of operator spaces. In this paper, the author investigates the duality for quantum spaces equipped with quantum bornologies. Particularly, it is shown that a finite complete bornology admits one unique quantization and any complete quantum space is a matrix bornology quotient of a local trace class algebra.
scientific article; zbMATH DE number 5989939