Abstract In this article, we give a sufficient and necessary condition for every Jordan {g,h}-derivation to be a {g,h}-derivation on triangular algebras. As an application, we prove that every Jordan {g,h}-derivation on τ ( N ) \tau ({\mathscr{N}}) is a {g,h}-derivation if and only if dim 0 + ≠ 1 \dim {0}_{+}\ne 1 or dim H − ⊥ ≠ 1 \dim {H}_{-}^{\perp }\ne 1 , where N {\mathscr{N}} is a non-trivial nest on a complex separable Hilbert space H and τ ( N ) \tau ({\mathscr{N}}) is the associated nest algebra.

中文翻译：

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Jordan {g,h}-三角代数的推导

摘要 在本文中，我们给出了每个 Jordan {g,h}-导数是三角代数上的 {g,h}-导数的充分必要条件。作为应用，我们证明τ ( N ) \tau ({\mathscr{N}}) 上的每一个Jordan {g,h}-导数都是{g,h}-导数当且仅当dim 0 + ≠ 1 \dim {0}_{+}\ne 1 或 dim H − ⊥ ≠ 1 \dim {H}_{-}^{\perp }\ne 1 ，其中 N {\mathscr{N}} 是非-一个复杂的可分离希尔伯特空间 H 上的平凡嵌套，τ ( N ) \tau ({\mathscr{N}}) 是相关的嵌套代数。