Let ℋ and $${\cal K}$$ K be complex infinite dimensional separable Hilbert spaces. We denote by $${M_C} = \left( {\begin{array}{*{20}{c}} A&C \\ 0&B \end{array}} \right)$$ M C = ( A C 0 B ) a 2 × 2 upper triangular operator matrix acting on $${\cal H} \oplus {\cal K}$$ ℋ ⊕ K , where $$A \in {\cal B}\left({\cal H} \right),\,B \in {\cal B}\left({\cal K} \right)$$ A ∈ ℬ ( ℋ ) , B ∈ ℬ ( K ) and $$C \in {\cal B}\left({{\cal K},{\cal H}} \right)$$ C ∈ ℬ ( K , ℋ ) . In this paper, we investigate the Weylness and generalized Weylness of M C for some (or every) $$C \in {\cal B}\left({{\cal K},{\cal H}} \right)$$ C ∈ ℬ ( K , ℋ ) .

中文翻译：

---

上三角算子矩阵的（广义）Weylness

令 ℋ 和 $${\cal K}$$ K 是复数无限维可分希尔伯特空间。我们用 $${M_C} = \left( {\begin{array}{*{20}{c}} A&C \\ 0&B \end{array}} \right)$$ MC = ( AC 0 B ) a作用于 $${\cal H} \oplus {\cal K}$$ ℋ ⊕ K 的 2 × 2 上三角算子矩阵，其中 $$A \in {\cal B}\left({\cal H} \right ),\,B \in {\cal B}\left({\cal K} \right)$$ A ∈ ℬ ( ℋ ) , B ∈ ℬ ( K ) and $$C \in {\cal B}\ left({{\cal K},{\cal H}} \right)$$ C ∈ ℬ ( K , ℋ ) 。在本文中，我们研究了某些（或每个）$$C \in {\cal B}\left({{\cal K},{\cal H}} \right)$$ 的 MC 的 Weylness 和广义 Weylness C ∈ ℬ ( K , ℋ ) 。