题目：Abundance Of Irreducible Tensor Product of Linear Operators
报告人：Prof. Caixing Gu （California Polytechnic State University）
摘要：The subspace of symmetric tensors and the subspace of anti-symmetric tensors are two natural reducing subspaces of tensor product A⊗I+I⊗A and A⊗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 A⊗I+I⊗A is a dense G_δ set in B(H). This generalizes Halmos’s theorem that the set of irreducible operators is a dense G_δ set in B(H). The same question for A⊗A is still open.
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