A remark on non-commutative $L^p$-spaces

Abstract

We explicitly describe the Haagerup and the Kosaki non-commutative $L^p$-spaces associated with a tensor product von Neumann algebra $M_1\bar{\otimes }{M}_2$ in terms of those associated with $M_i$ and usual tensor products of unbounded operators. The descriptions are then shown to be useful in the quantum information theory based on operator algebras.

v2; references added

References in corpus (2)

• Entropic Fluctuations in Quantum Statistical Mechanics. An Introduction
• The strong converse exponent of discriminating infinite-dimensional quantum states