Date | 2019-06-14 |
---|---|

Speaker | Caixing Gu |

Dept. | California Polytechnic State University |

Room | 27-116 |

Time | 15:00-17:00 |

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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