Commutative subalgebras of the algebra of smooth operators

2015/03/24 by Ciaś, Tomasz
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1503.07095

Abstract

We consider the Fréchet ^*-algebra L(s',s) of the so-called smooth operators, i.e. continuous linear operators from the dual s' of the space s of rapidly decreasing sequences into s. This algebra is a non-commutative analogue of the algebra s. We characterize all closed commutative ^*-subalgebras of L(s',s) which are at the same time isomorphic to closed ^*-subalgebras of s and we provide an example of a closed commutative ^*-subalgebra of L(s',s) which cannot be embedded into s.

Related

• On the algebra of smooth operators
• Smooth *-algebras
• Separation Theorems in Smooth Commutative Algebra and Applications
• Monotone operator functions on C^*-algebra
• Differential operators on non-commutative algebras