On bounded Dual-valued derivations on certain Banach algebras
On strongly closed subalgebras of B(X)
On the algebra of smooth operators
Let s be the space of rapidly decreasing sequences. We give the spectral representation of normal elements in the Fréchet algebra L(s',s) of so-called smooth operators. We also characterize closed commutative *-subalgebras of L(s',s) and establish a Hölder continuous functional calculus in this algebra. The key tool is the property (DN) of s.
On the locally -convex algebra and a differential-geometric interpretation of it.