Abstract
It is shown that if a symmetric Banach space E on the positive semi-axis is p-convex (q-concave) then so is the corresponding non-commutative symmetric space E(τ) of τ-measurable operators affiliated with some semifinite von Neumann algebra \({({\mathcal{M}}, \tau)}\) , with preservation of the convexity (concavity) constants in the case that \({{\mathcal{M}}}\) is non-atomic. Similar statements hold in the case that E satisfies an upper (lower) p-estimate and extend to the more general semifinite setting earlier results due to Arazy and Lin for unitary matrix spaces.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.