On Gelfand-Naimark type Theorems for unital abelian complex and real locally C*-, and locally JB-algebras

A Note on Symmetry of Birkhoff-James Orthogonality in Positive Cones of Locally C*-algebras

“…where each B α is a commutative unital C * -subalgebra of A α . Using a Gelfand-Naimark type theorem for commutative locally C * -algebras (see [27]) we get a functional locally C * -algebra C(X) of type Λ of all continuous complex-valued functions on compactly generated completely regular topological space X with generating family of Hausdorff compacts X α , such that B ∼ = C(X), Mathematics 2020, 8, 1027 13 of 14 for each α ∈ Λ, and…”