“…In recent years a lot of work has been done on Kaplansky's problem [4] of characterizing linear maps preserving invertibility (see [1] for some historical remarks). The aim of this note is to provide a simple proof of a result of Jafarian and Sourour [3] on linear invertibility preserving maps acting between operator algebras B(X) and B(Y ).…”
Section: Introduction and Statement Of Resultsmentioning
“…In recent years a lot of work has been done on Kaplansky's problem [4] of characterizing linear maps preserving invertibility (see [1] for some historical remarks). The aim of this note is to provide a simple proof of a result of Jafarian and Sourour [3] on linear invertibility preserving maps acting between operator algebras B(X) and B(Y ).…”
Section: Introduction and Statement Of Resultsmentioning
“…Additional related results are in [1], [4], [10] and [18]. In [1, p. 30], Aupetit obtained a result which contains the Dieudonné-Marcus-Purves result and the Gleason-Kahane-Zelazko result.…”
Section: (B) φ Is a Jordan Isomorphism (C) φ Is Either An Isomorphismentioning
Abstract. For Banach spaces X and Y , we show that every unital bijective invertibility preserving linear map between L(X) and L(Y ) is a Jordan isomorphism. The same conclusion holds for maps between CI + K(X) and CI + K(Y ).
“…According to [3,Cor.4,p.143], symmetric Banach * -algebras are in S sa . Recall that a Banach * -algebra is symmetric if every self-adjoint element has real spectrum.…”
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