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Linear Maps Preserving Generalized Invertibility |
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| Authors: | Mostafa Mbekhta Leiba Rodman Peter Šemrl |
| Institution: | (1) UFR de Mathématiques, Université de Lille I, F-59655 Villeneuve d’Ascq Cedex, Lille, France;(2) Department of Mathematics, The College of William and Mary, Williamsburg, VA 23187-8795, USA;(3) Department of Mathematics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia |
| Abstract: | Let H be an infinite-dimensional complex separable Hilbert space and
the algebra of all bounded linear operators on H. Let
be a bijective continuous unital linear map preserving generalized invertibility in both directions. Then the ideal of all
compact operators is invariant under ϕ and the induced linear map on the Calkin algebra is either an automorphism or an antiautomorphism. |
| Keywords: | 47B49 47L99 |
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