Open Access

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

### Abstract

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.

Key words: Kaplansky-Hilbert module, $L^0$-linear operator, unbounded operator, O*-algebra, automorphism, derivation.

### Article Information

 Title Algebras of unbounded operators over the ring of measurable functions and their derivations and automorphisms Source Methods Funct. Anal. Topology, Vol. 15 (2009), no. 2, 177-187 MathSciNet MR2553533 Copyright The Author(s) 2009 (CC BY-SA)

### Authors Information

S. Albeverio
Institut fur Angewandte Mathematik, Universitat Bonn, Wegelerstr. 6, D--53115, Bonn, Germany; SFB 611, Bonn, Germany; BiBoS, Bielefeld, Germany; CERFIM, Locarno and USI, Switzerland

Sh. A. Ayupov
Institute of Mathematics and Information Technologies, Uzbekistan Academy of Sciences, 29 F. Hodjaev str., Tashkent, 100125, Uzbekistan

A. A. Zaitov
Institute of Mathematics and Information Technologies, Uzbekistan Academy of Sciences, 29 F. Hodjaev str., Tashkent, 100125, Uzbekistan

J. E. Ruziev
Institute of Mathematics and Information Technologies, Uzbekistan Academy of Sciences, 29 F. Hodjaev str., Tashkent, 100125, Uzbekistan

### Citation Example

S. Albeverio, Sh. A. Ayupov, A. A. Zaitov, and J. E. Ruziev, Algebras of unbounded operators over the ring of measurable functions and their derivations and automorphisms, Methods Funct. Anal. Topology 15 (2009), no. 2, 177-187.

### BibTex

@article {MFAT446,
AUTHOR = {Albeverio, S. and Ayupov, Sh. A. and Zaitov, A. A. and Ruziev, J. E.},
TITLE = {Algebras of unbounded operators over the ring of measurable functions and their derivations and automorphisms},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {15},
YEAR = {2009},
NUMBER = {2},
PAGES = {177-187},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=446},
}