Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Different Types of Conditional Expectation and the Lueders - von Neumann
  Quantum Measurement   In operator algebra theory, a conditional expectation is usually assumed to
be a projection map onto a sub-algebra. In the paper, a further type of
conditional expectation and an extension of the Lueders - von Neumann
measurement to observables with continuous spectra are considered; both are
defined for a single operator and become a projection map only if they exist
for all operators. Criteria for the existence of the different types of
conditional expectation and of the extension of the Lueders - von Neumann
measurement are presented, and the question whether they coincide is studied.
All this is done in the general framework of Jordan operator algebras. The
examples considered include the type I and type II operator algebras, the
standard Hilbert space model of quantum mechanics, and a no-go result
concerning the conditional expectation of observables that satisfy the
canonical commutator relation.

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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin