Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: L$^p$ spaces of operator-valued functions   We define a p-norm in the context of quantum random variables, measurable
operator-valued functions with respect to a positive operator-valued measure.
This norm leads to a operator-valued L^p space that is shown to be complete.
Various other norm candidates are considered as well as generalizations of
H\"older's inequality to this new context.

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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs
20
The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con