Geodesic
Maps on the Algebras of Measurable Operators Preserving Zero and Jordan Zero-products
Dalʹnevostočnyj matematičeskij žurnal, Tome 12 (2012) no. 2, pp. 195-200.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we prove that a continuous linear surjection from an algebra of measurable operators onto another one preserves zero products (resp. zero Jordan products) if and only if it is a non-zero scalar multiple of a homomorphism (resp. of an Jordan homomorphism). 
@article{DVMG_2012_12_2_a6,
     author = {I. M. Juraev},
     title = {Maps on the {Algebras} of {Measurable} {Operators} {Preserving} {Zero} and {Jordan} {Zero-products}},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {195--200},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2012_12_2_a6/}
}
TY  - JOUR
AU  - I. M. Juraev
TI  - Maps on the Algebras of Measurable Operators Preserving Zero and Jordan Zero-products
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2012
SP  - 195
EP  - 200
VL  - 12
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2012_12_2_a6/
LA  - ru
ID  - DVMG_2012_12_2_a6
ER  - 
%0 Journal Article
%A I. M. Juraev
%T Maps on the Algebras of Measurable Operators Preserving Zero and Jordan Zero-products
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2012
%P 195-200
%V 12
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2012_12_2_a6/
%G ru
%F DVMG_2012_12_2_a6
I. M. Juraev. Maps on the Algebras of Measurable Operators Preserving Zero and Jordan Zero-products. Dalʹnevostočnyj matematičeskij žurnal, Tome 12 (2012) no. 2, pp. 195-200. http://geodesic.mathdoc.fr/item/DVMG_2012_12_2_a6/

[1] S. K. Berberian, “The regular ring of finite $AW^*$-algebra”, Ann. Math, 65 (1957), 224–242 | DOI | MR

[2] M. A. Chebotar, Wen-Fong Ke, Pjek-Hwee Lee, “Maps characterized by action on zero products”, Pacific J.Math., 216:2 (2004), 217–228 | DOI | MR | Zbl

[3] M. A. Chebotar, Wen-Fong Ke, Pjek-Hwee Lee, Ruibin Zhand, “On maps preserving zero Jordan products”, Monatsh. Math., 149 (2006), 91–101 | DOI | MR | Zbl

[4] J. Cui, J. Hou, “Linear maps on von Neumann algebras preserving zero products or TR-rank”, Bull. Austral. Math. Soc., 65 (2002), 79–91 | DOI | MR | Zbl

[5] J. Cui, J. Hou, “Characterizations of nest algebra automorphisms”, Chinese Ann. Math. (to appear)

[6] J. Hou, M. Gao, “Additive mappings on $B(H)$ that preserve zero products”, Kexue Tongbao (Chinese), 43 (1998), 2388–2392 | MR

[7] M. A. Muratov, V. I. Chilin, Algebry izmerimykh i lokalno izmerimykh operatorov, v. 69, Pratsi In-tu matematiki NAN Ukraini, Kiiv, 2007, 390 pp. | Zbl

[8] P. Semrl, “Linear mappings preserving square-zero matrices”, Bull. Austral. Math. Soc., 48 (1993), 365–370 | DOI | MR | Zbl

[9] L. Zhao, J. Hou, “Jordan zero product preserving additive maps on operator algebras”, J. Math. Anal. Appl., 314 (2006), 689–700 | DOI | MR | Zbl