Some remarks on derivations on the algebra of operators in Hilbert pro-C*-bimodules

2016/12/10 by Karimi, Khadijeh, Sharifi, Kamran
#46H25 #47B47 #FOS: Mathematics #Operator Algebras (math.OA) #Primary 46L08 #Secondary 46L05

paper · doi:10.48550/arxiv.1612.03282

Abstract

Suppose A is a pro-C*-algebra. Let L_A(E) be the pro-C*-algebra of adjointable operators on a Hilbert A-module E and let K_A(E) be the closed two sided *-ideal of all compact operators on E. We prove that if E be a full Hilbert A-module, the innerness of derivations on K_A(E) implies the innerness of derivations on L_A(E). We show that if A is a commutative pro-C*-algebra and E is a Hilbert A-bimodule then every derivation on K_A(E) is zero. Moreover, if A is a commutative σ-C*-algebra and E is a Hilbert A-bimodule then every derivation on L_A(E) is zero, too.

Related

• Derivations, local and 2-local derivations on some algebras of operators on Hilbert C*-modules
• The C*-algebra of a Hilbert Bimodule
• Restricting operators to thick Hilbert C*-submodules
• Injective and projective Hilbert C*-modules, and C*-algebras of compact operators
• Derivations in the Banach ideals of τ-compact operators