AN EXTENSION OF A TERNARY DERIVATION ON A HILBERT C* -MODULE

Abstract. Let E be a Hilbert module over a C* -algebra B. A ternary derivation of E is a densely defined linear map δ : D( δ ) Ì E® E that fulfills : d(xáy, zñ) = d (x)áy, zñ + xá d(y), zñ + xáy, d (z)ñ (x, y, z ϵ E), where D(d )áD(d ) , D(d)ñ Ì D(d ), that is, D( d) is invariant under the ternary product (x, y, z) ® xáy, zñ. In this talk we extend each ternary derivation of a full Hilbert B-module E to a derivation D on the linking algebra of E and investigate the relation between d and D . In particular we show that d is a generator of a dynamical system on E if and only if D is a generator of a C* -dynamical system on the linking algebra.

کلیدواژه ها:

Hilbert module ، derivation ، dynamical system