A Note on Sequential Product of Quantum Effects

Chunyuan Deng

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: The quantum effects for a physical system can be described by the set ℰ(ℋ) of positive operators on a complex Hilbert space ℋ that are bounded above by the identity operator I. For A, B ∈ ℰ(ℋ), let A∘B = A1/2BA1/2 be the sequential product and let A*B = (AB + BA)/2 be the Jordan product of A, B ∈ ℰ(ℋ). The main purpose of this note is to study some of the algebraic properties of effects. Many of our results show that algebraic conditions on A∘B and A*B imply that A and B have 3 × 3 diagonal operator matrix forms with Iℛ(A)¯∩ℛ(B)¯ as an orthogonal projection on closed subspace ℛ(A)¯∩ℛ(B)¯ being the common part of A and B. Moreover, some generalizations of results known in the literature and a number of new results for bounded operators are derived.

Date: 2013
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https://doi.org/10.1155/2013/520436

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:520436

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