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Abundance of irreducible tensor product of linear operators

이우영 0 2802
구분 초청강연
일정 2019-06-14 15:00 ~ 17:00
강연자 Caixing Gu (California Polytechnic State University)
기타
담당교수 이우영
The subspace of symmetric tensors and the subspace of anti-symmetric tensors are two natural reducing subspaces of tensor product $Aotimes I+Iotimes A$ and $Aotimes A$ for any bounded linear operator $A$ on a complex separable Hilbert space $H$. We show the set of operators $A$ such that these two subspaces are the only (nontrivial) reducing subspaces of $Aotimes I+Iotimes A$ is a dense $G_{delta}$ set in $B(H).$ This generalizes Halmos`s theorem that the set of irreducible operators is a dense $G_{delta}$ set in $B(H).$ The same question for $Aotimes A$ is still open.

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