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

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

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

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Description

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.