Orthogonally additive polynomials on non-commutative \(L^p\)-spaces

  • Jerónimo Alaminos
  • María L. C. Godoy
  • Armando R. VillenaEmail author


Let \({{\mathscr {M}}}\) be a von Neumann algebra with a normal semifinite faithful trace \(\tau \). We prove that every continuous m-homogeneous polynomial P from \(L^p({{\mathscr {M}}},\tau )\), with \(0<p<\infty \), into each topological linear space X with the property that \(P(x+y)=P(x)+P(y)\) whenever x and y are mutually orthogonal positive elements of \(L^p({{\mathscr {M}}},\tau )\) can be represented in the form \(P(x)=\varPhi (x^m)\)\((x\in L^p({{\mathscr {M}}},\tau ))\) for some continuous linear map \(\varPhi :L^{p/m}({{\mathscr {M}}},\tau )\rightarrow X\).


Non-commutative \(L^p\)-space Schatten classes Orthogonally additive polynomial 

Mathematics Subject Classification

46L10 46L52 47H60 



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Copyright information

© Universidad Complutense de Madrid 2019

Authors and Affiliations

  • Jerónimo Alaminos
    • 1
  • María L. C. Godoy
    • 1
  • Armando R. Villena
    • 1
    Email author
  1. 1.Departamento de Análisis Matemático, Facultad de CienciasUniversidad de GranadaGranadaSpain

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