Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unconditionality with respect to orthonormal systems in noncommutative
  $L_2$ spaces   Orthonormal systems in commutative $L_2$ spaces can be used to classify
Banach spaces. When the system is complete and satisfies certain norm condition
the unconditionality with respect to the system characterizes Hilbert spaces.
As a noncommutative analogue we introduce the notion of unconditionality of
operator spaces with respect to orthonormal systems in noncommutative $L_2$
spaces and show that the unconditionality characterizes operator Hilbert spaces
when the system is complete and satisfy certain norm condition. The proof of
the main result heavily depends on free probabilistic tools such as contraction
principle for $*$-free Haar unitaries, comparision of averages with respect to
$*$-free Haar unitaries and $*$-free circular elements and $K$-covexity, type 2
and cotype 2 with respect to $*$-free circular elements.

34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th