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

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

2007-10-31

arxiv.org/abs/0710.5839v1

Mathematics

Functional Analysis

Scientific paper

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.

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