Algebras of unbounded operators over the ring of measurable functions and their derivations and automorphisms

S. Albeverio, Sh. A. Ayupov, A. A. Zaitov, J. E. Ruziev

Published 2007-10-31Version 1

In the present paper derivations and *-automorphisms of algebras of unbounded operators over the ring of measurable functions are investigated and it is shown that all L^0-linear derivations and L^{0}-linear *-automorphisms are inner. Moreover, it is proved that each L^0-linear automorphism of the algebra of all linear operators on a bo-dense submodule of a Kaplansky-Hilbert module over the ring of measurable functions is spatial.