Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
Let X be an infinite-dimensional Banach space, and let ϕ be a surjective linear map on B(X) with ϕ(I) = I. If ϕ preserves injective operators in both directions then ϕ is an automorphism of the algebra B(X). If X is a Hilbert space, then ϕ is an automorphism of B(X) if and only if it preserves surjective operators in both directions.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
143-149
Opis fizyczny
Daty
wydano
1993
otrzymano
1992-06-11
poprawiono
1993-01-25
Twórcy
autor
- Department of Mathematics, University of Ljubljana, Jadranska 19, 61000 Ljubljana, Slovenia
Bibliografia
- [1] M. D. Choi, D. Hadwin, E. Nordgren, H. Radjavi, and P. Rosenthal, On positive linear maps preserving invertibility, J. Funct. Anal. 59 (1984), 462-469.
- [2] M. D. Choi, A. A. Jafarian, and H. Radjavi, Linear maps preserving commutativity, Linear Algebra Appl. 87 (1987), 227-241.
- [3] C. Davis and P. Rosenthal, Solving linear operator equations, Canad. J. Math. 26 (1974), 1384-1389.
- [4] J. C. Hou, Rank-preserving linear maps on B(X), Science in China (Ser. A) 32 (1989), 929-940.
- [5] A. A. Jafarian and A. R. Sourour, Spectrum-preserving linear maps, J. Funct. Anal. 66 (1986), 255-261.
- [6] I. Kaplansky, Infinite Abelian Groups, University of Michigan Press, Ann Arbor 1954.
- [7] K. B. Laursen and P. Vrbová, Some remarks on the surjectivity spectrum of linear operators, Czechoslovak Math. J. 39 (1989), 730-739.
- [8] J. Lindenstrauss, On nonseparable reflexive Banach spaces, Bull. Amer. Math. Soc. 72 (1966), 967-970.
- [9] M. Marcus and B. N. Moyls, Linear transformations on algebras of matrices, Canad. J. Math. 11 (1959), 61-66.
- [10] M. Omladič, On operators preserving commutativity, J. Funct. Anal. 66 (1986), 105-122.
- [12] R. I. Ovsepian and A. Pełczyński, Existence of a fundamental total and bounded biorthogonal sequence, Studia Math. 54 (1975), 149-159.
- [13] C. Pearcy and D. Topping, Sums of small number of idempotents, Michigan Math. J. 14 (1967), 453-465.
- [14] H. Radjavi and P. Rosenthal, Invariant Subspaces, Ergeb. Math. Grenzgeb. 77, Springer, Berlin 1973.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
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