Year: 2025
Type: preprint
Abstract: We study unital operator spaces endowed with a partially defined product. We give a matrix-norm characterization of such products that allows for a representation theorem where the partial product is realized as composition of operators on Hilbert space. We study product-respecting C*-covers, including a universal product C*-cover, and product quotients. We show that for the Haagerup tensor product of unital operator spaces remains injective, while projectivity holds relative to product quotients. Moreover, we identify the commuting tensor product as a complete product quotient of the Haagerup tensor product. Our framework yields new factorization norm formulas for a variety of product structures, as well as an intrinsic trace-extension criterion that resolves a question posed by Sinclair. Our work unifies and extends tensor products for operator systems, with applications in quantum information theory.
Source: arXiv (Cornell University)
Authors: Dor-On, Adam, Russell, Travis B.
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4416025561
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