arXiv subjects

Arunkumar C. S

Publications and source records attributed to Arunkumar C. S.

2 recordsLinked to original sources

arXiv2021

Local boundary representations of locally C*-algebras

We initiate a study of non-commutative Choquet boundary for spaces of unbounded operators. We define the notion of local boundary representations for local operator systems in locally C$^*$-algebras and prove that local boundary representations provide an intrinsic invariant for a particular class of local operator systems. An appropriate analog of purity of local completely positive maps on local operator systems is used to characterize local boundary representations for local operator systems in Frechet locally C$^*$-algebras.

math.OA↗

arXiv2021

Boundary Representations and Rectangular Hyperrigidity

We explore connections between boundary representations of operator spaces and those of the associated Paulsen systems. Using the notions of finite representation and separating property which we introduced, boundary representations for operator spaces is characterised. We also introduce weak boundary for operator spaces. Rectangular hyperrigidity of operator spaces introduced here is used to establish an analogue of Saskin's theorem in the setting of operator spaces in finite dimensions.

math.OA↗