Polynomials in operator space theory: matrix ordering and algebraic aspects
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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.
KeywordsMatrix regular operator spaces Operator systems Tensor products Ideals
Mathematics Subject ClassificationPrimary 46L06 46L07 Secondary 46L05 47L25
The authors would like to thank Andreas Defant for providing a copy of . The authors would also like to thank the referee for useful comments and suggestions.
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