@article{bwmeta1.element.bwnjournal-article-bcpv38i1p49bwm,
author = {Bre\v sar, Matej and \v Semrl, Peter},
title = {Linear preservers on B(X)},
journal = {Banach Center Publications},
volume = {38},
year = {1997},
pages = {49-58},
zbl = {0939.47031},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv38i1p49bwm}
}
Brešar, Matej; Šemrl, Peter. Linear preservers on ℬ(X). Banach Center Publications, Tome 38 (1997) pp. 49-58. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv38i1p49bwm/
[000] [1] A survey of linear preserver problems, Linear and Multilinear Algebra 33 (1992), 1-129.
[001] [2] B. Aupetit, A primer on spectral theory, Universitext, Springer, New York, 1991.
[002] [3] B. Aupetit and H. du T. Mouton, Spectrum-preserving linear mappings in Banach algebras, Studia Math. 109 (1994), 91-100. | Zbl 0829.46039
[003] [4] M. Brešar, Commuting traces of biadditive mappings, commutativity-preserving mappings and Lie mappings, Trans. Amer. Math. Soc. 335 (1993), 525-546. | Zbl 0791.16028
[004] [5] M. Brešar and C. R. Miers, Commutativity preserving mappings of von Neumann algebras, Canad. J. Math. 45 (1993), 695-708. | Zbl 0794.46045
[005] [6] M. Brešar and P. Šemrl, Mappings which preserve idempotents, local automorphisms, and local derivations, Canad. J. Math. 45 (1993), 483-496. | Zbl 0796.15001
[006] [7] M. Brešar, P. Šemrl, Normal-preserving linear mappings, Canad. Math. Bull. 37 (1994), 306-309. | Zbl 0816.47018
[007] [8] M. Brešar, P. Šemrl, On local automorphisms and mappings that preserve idempotents, Studia Math. 113 (1995), 101-108. | Zbl 0835.47020
[008] [9] M. Brešar, P. Šemrl, Linear maps preserving the spectral radius, J. Funct. Anal. 142 (1996), 360-368. | Zbl 0873.47002
[009] [10] M. D. Choi, A. A. Jafarian and H. Radjavi, Linear maps preserving commutativity, Linear Algebra Appl. 87 (1987), 227-241. | Zbl 0615.15004
[010] [11] H. A. Dye, On the geometry of projections in certain operator algebras, Ann. of Math. (2) 61 (1955), 73-89. | Zbl 0064.11002
[011] [12] G. Frobenius, Über die Darstellung der endlichen Gruppen durch lineare Substitutionen, Sitzungsber. Deutsch. Akad. Wiss. Berlin (1897), 994-1015. | Zbl 28.0130.01
[012] [13] I. N. Herstein, Rings with involution, University of Chicago Press, Chicago, 1976.
[013] [14] I. N. Herstein, Topics in ring theory, University of Chicago Press, Chicago, 1969. | Zbl 0232.16001
[014] [15] J. C. Hou, Rank preserving linear maps on B(X), Sci. China Ser. A 32 (1989), 929-940. | Zbl 0686.47030
[015] [16] N. Jacobson and C. E. Rickart, Jordan homomorphisms of rings, Trans. Amer. Math. Soc. 69 (1950), 479-502. | Zbl 0039.26402
[016] [17] A. A. Jafarian and A. R. Sourour, Spectrum-preserving linear maps, J. Funct. Anal. 66 (1986), 255-261. | Zbl 0589.47003
[017] [18] I. Kaplansky, Algebraic and analytic aspects of operator algebras, Regional Conference Series in Mathematics 1, Amer. Math. Soc., Providence, 1970. | Zbl 0217.44902
[018] [19] C.-K. Li and N.-K. Tsing, Linear preserver problems: A brief introduction and some special techniques, Linear Algebra Appl. 162-164 (1992), 217-235.
[019] [20] M. Marcus, Linear operations on matrices, Amer. Math. Monthly 69 (1962), 837-847. | Zbl 0108.01104
[020] [21] W. S. Martindale, Prime rings satisfying a generalized polynomial identity, J. Algebra 12 (1969), 576-584. | Zbl 0175.03102
[021] [22] M. Omladič, On operators preserving commutativity, J. Funct. Anal. 66 (1986), 105-122. | Zbl 0587.47051
[022] [23] M. Omladič, On operators preserving the numerical range, Linear Algebra Appl. 134 (1990), 31-51. | Zbl 0716.47004
[023] [24] M. Omladič and P. Šemrl, Spectrum-preserving additive maps, ibid. 153 (1991), 67-72.
[024] [25] M. Omladič, P. Šemrl, Additive mappings preserving operators of rank one, ibid. 182 (1993), 239-256. | Zbl 0803.47026
[025] [26] M. Omladič, P. Šemrl, Linear mappings that preserve potent operators, Proc. Amer. Math. Soc. 123 (1995), 1069-1074. | Zbl 0831.47026
[026] [27] C. Pearcy and D. Topping, Sums of small numbers of operators, Michigan Math. J. 14 (1967), 453-465.
[027] [28] H. Radjavi and P. Rosenthal, Invariant subspaces, Ergeb. Math. Grenzgeb. 77, Springer, Berlin, 1973.
[028] [29] B. Russo and H. A. Dye, A note on unitary operators in C*-algebras, Duke Math. J. 33 (1966), 413-416. | Zbl 0171.11503
[029] [30] P. Šemrl, Two characterizations of automorphisms on B(X), Studia Math. 105 (1993), 143-149.
[030] [31] P. Šemrl, Linear maps that preserve the nilpotent operators, Acta Sci. Math. (Szeged) 61 (1995), 523-534. | Zbl 0843.47024
[031] [32] A. R. Sourour, Invertibility preserving linear maps on L(X), preprint. | Zbl 0843.47023
[032] [33] A. R. Sourour, The Gleason-Kahane-Żelazko theorem and its generalizations, Banach Center Publ. 30 (1994), 327-331. | Zbl 0813.47044
[033] [34] W. Watkins, Linear maps that preserve commuting pairs of matrices, Linear Algebra Appl. 14 (1976), 29-35. | Zbl 0329.15005