Completely Complemented Subspace Problem
نویسنده
چکیده
Communicated by Abstract. We will prove that, if every finite dimensional subspace of an infinite dimensional operator space E is 1-completely complemented in it, E is 1-Hilbertian and 1-homogeneous. However, this is not true for finite dimensional operator spaces: we give an example of an n-dimensional operator space E, such that all of its subspaces are 1-completely complemented in E, but which is not 1-homogeneous. Moreover, we will show that, if E is an operator space such that both E and E∗ are c-exact and every subspace of E is λ-completely complemented in it, then E is f(c, λ)-completely isomorphic either to row or column operator space.
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