English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Orthonormal systems in commutative $L_2$ spaces can be used to classifyBanach spaces. When the system is complete and satisfies certain norm conditionthe unconditionality with respect to the system characterizes Hilbert spaces.As a noncommutative analogue we introduce the notion of unconditionality ofoperator spaces with respect to orthonormal systems in noncommutative $L_2$spaces and show that the unconditionality characterizes operator Hilbert spaceswhen the system is complete and satisfy certain norm condition. The proof ofthe main result heavily depends on free probabilistic tools such as contractionprinciple for $*$-free Haar unitaries, comparision of averages with respect to$*$-free Haar unitaries and $*$-free circular elements and $K$-covexity, type 2and cotype 2 with respect to $*$-free circular elements.

Unconditionality with respect to orthonormal systems in noncommutative $L_2$ spaces