2-local Jordan automorphisms on operator algebras
Tom 209 / 2012
Studia Mathematica 209 (2012), 235-246
MSC: Primary 16W20; Secondary 47L10.
DOI: 10.4064/sm209-3-3
Streszczenie
We investigate $2$-local Jordan automorphisms on operator algebras. In particular, we show that every $2$-local Jordan automorphism of the algebra of all $n\times n$ real or complex matrices is either an automorphism or an anti-automorphism. The same is true for $2$-local Jordan automorphisms of any subalgebra of $\mathcal B$ which contains the ideal of all compact operators on $X$, where $X$ is a real or complex separable Banach spaces and $\mathcal B$ is the algebra of all bounded linear operators on $X$.