, Volume 22, Issue 2, pp 629–652 | Cite as

Polynomials in operator space theory: matrix ordering and algebraic aspects

  • Preeti Luthra
  • Ajay Kumar
  • Vandana Rajpal


We extend the \(\lambda \)-theory of operator spaces given in Defant and Wiesner (J. Funct. Anal. 266(9): 5493–5525, 2014), that generalizes the notion of the projective, Haagerup and Schur tensor norm for operator spaces to matrix ordered spaces and Banach \(*\)-algebras. Given matrix regular operator spaces and operator systems, we introduce cones related to \(\lambda \) for the algebraic operator space tensor product that respect the matricial structure of matrix regular operator spaces and operator systems, respectively. The ideal structure of \(\lambda \)-tensor product of \(C^*\)-algebras has also been discussed.


Matrix regular operator spaces Operator systems Tensor products Ideals 

Mathematics Subject Classification

Primary 46L06 46L07 Secondary 46L05 47L25 



The authors would like to thank Andreas Defant for providing a copy of [19]. The authors would also like to thank the referee for useful comments and suggestions.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of DelhiDelhiIndia
  2. 2.Department of Mathematics, Shivaji CollegeUniversity of DelhiDelhiIndia

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