Differential Banach *-Algebras of Compact Operators Associated with Symmetric Operators

Extensive development of noncommutative geometry requires elaboration of the theory of differential Banach *-algebras, that is, dense *-subalgebras of C*-algebras whose properties are analogous to the properties of algebras of differentiable functions. We consider a specific class of such algebras,D-algebras, and show that various *-algebras of compact operators associated with symmetric operatorsSon Hilbert spacesHareD-subalgebras of the C*-algebra of all compact operatorsC(H). We focus on how the properties of the operatorsSare reflected in the structure of these operator algebras.