A quantum Banach space (operator space for short) is a linear subspace of Hilbert space operators together with its induced matrix norm structure. It is said to be a quantum operator algebra (operator algebra for short) if it is closed under multiplication.

In a joint work with Matt Neal, a necessary and sufficient condition is given for a operator space to support a multiplication making it quantum isomorphic to a unital operator algebra. The condition involves only the holomorphic structure of the matrix spaces with entries from the operator space. The proof involves an algebraic structure which is equivalent to the holomorphic structure.