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Additive maps preserving rank-one operators on nest algebras. (English) Zbl 1193.47038

In the present paper, the authors study the structure of additive maps preserving rank-one operators in both directions on nest algebras over Banach spaces. A description of linear maps preserving rank one operators on nest algebras over Hilbert spaces was given in [J.-L.Cui and J.-C.Hou, Acta Math.Sin., Engl.Ser.20 (5), 807–820 (2004; Zbl 1085.47047)]. We may also mention the papers by S.-Y.Wei and S.-Z.Hou [J. Oper.Theory 39 (2), 207–217 (1998; Zbl 0998.47047)] and J.-C.Hou and J.-L.Cui [Linear Algebra Appl.369, 263–277 (2003; Zbl 1054.47029)], where linear maps preserving rank one operators on nest algebras acting on Banach spaces were investigated. Finally, it is worth noting that a thorough characterization of additive rank one preservers on triangular matrix algebras was given by J.Bell and A.R.Sourour [Linear Algebra Appl.312, 13–33 (2000; Zbl 0962.15002)].

MSC:

47B49 Transformers, preservers (linear operators on spaces of linear operators)
47L35 Nest algebras, CSL algebras
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[1] DOI: 10.1016/S0024-3795(00)00024-0 · Zbl 0962.15002 · doi:10.1016/S0024-3795(00)00024-0
[2] DOI: 10.1016/S0024-3795(97)00069-4 · Zbl 0886.15004 · doi:10.1016/S0024-3795(97)00069-4
[3] Cui J, Lin. Alg. Appl. 377 pp 267– (2004) · Zbl 1055.47033 · doi:10.1016/j.laa.2003.08.017
[4] Cui J, Lin. Alg. Appl. 336 pp 29– (2001) · Zbl 1015.47015 · doi:10.1016/S0024-3795(01)00288-9
[5] DOI: 10.1007/s10114-004-0314-6 · Zbl 1085.47047 · doi:10.1007/s10114-004-0314-6
[6] Davision KR, Nest Algebras, Pitman Research Notes in Mathematics 191 (1988)
[7] Hou J, Sci. China ser. A 32 pp 929– (1989)
[8] Hou J, Lin. Alg. Appl. 369 pp 263– (2003) · Zbl 1054.47029 · doi:10.1016/S0024-3795(02)00725-5
[9] Hou J, Proc. Amer. Math. Soc. 132 pp 1419– (2004) · Zbl 1058.47031 · doi:10.1090/S0002-9939-03-07275-7
[10] Molnár L, J. Func. Anal. 144 pp 248– (2002) · Zbl 1010.46023 · doi:10.1006/jfan.2002.3970
[11] DOI: 10.1080/03081089808818586 · Zbl 0974.15001 · doi:10.1080/03081089808818586
[12] DOI: 10.1016/0024-3795(93)90502-F · Zbl 0803.47026 · doi:10.1016/0024-3795(93)90502-F
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