Operator System Structures and Extensions of Schur Multipliers

Lin, Ying-Fen; Todorov, Ivan G.

doi:10.1093/imrn/rnz364

Cited by 1 publication

(2 citation statements)

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“…Dual operator A-systems are dual operator systems that also carry an "A-compatible" operator system structure. They were introduced in [25]. We prove that the coproducts of dual operator A-systems are also dual operator A-systems (Theorem 5.5).…”

Section: Introductionmentioning

confidence: 91%

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On coproducts of operator $\mathcal{A}$-systems

Alexandros¹

2022

Preprint

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Given a unital C * -algebra A, we prove the existence of the coproduct of two faithful operator A-systems. We show that we can either consider it as a subsystem of an amalgamated free product of C * -algebras, or as a quotient by an operator system kernel. We introduce a universal C * -algebra for operator A-systems and prove that in the case of the coproduct of two operator A-systems, it is isomorphic to the amalgamated over A, free product of their respective universal C * -algebras. Also, under the assumptions of hyperrigidity for operator systems, we can identify the C * -envelope of the coproduct with the amalgamated free product of the C * -envelopes. We consider graph operator systems as examples of operator A-systems and prove that there exist graph operator systems whose coproduct is not a graph operator system, it is however a dual operator A-system. More generally, the coproduct of dual operator A-systems is always a dual operator A-system. We show that the coproducts behave well with respect to inductive limits of operator systems.

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Section: Introductionmentioning

confidence: 91%

“…In order to see this, we need to prove first that their coproduct is w*-closed, and also that the module action is separately w*-continuous. For more about the subject, we refer to the work of Y-F. Lin and I. Todorov [25]. Definition 5.2.…”

Section: A Special Operator A-system and Dual Operator A-systemsmentioning

confidence: 99%

On coproducts of operator $\mathcal{A}$-systems

Alexandros¹

2022

Preprint

View full text Add to dashboard Cite

show abstract

Operator System Structures and Extensions of Schur Multipliers

Cited by 1 publication

References 22 publications

On coproducts of operator $\mathcal{A}$-systems

On coproducts of operator $\mathcal{A}$-systems

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