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.

Full Text

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},
  MRNUMBER = {MR2553533},
       URL = {http://mfat.imath.kiev.ua/article/?id=446},
}