论文标题
零产品确定Banach代数
Zero product determined Banach algebras
论文作者
论文摘要
令$ \ Mathcal {l} $为完全分布的换向子空间晶格或带有两个原子的子空间晶格，我们使用统一的方法来研究衍生物，$ \ Mathrm {alg} \ Mathcal {l Mathcal {l} $。我们验证$ \ mathrm {alg} \ Mathcal {l} \ cap \ mathcal {k}（\ Mathcal {h}）$的乘数代数是等异，至$ \ mathrm {alg}确定的产品。对于$ t $ in $ m_ {n}（\ mathbb {c}）$，$ n \ geq 2 $，我们表明$ \ mathcal {a} _ {t} $是零产品，并且仅当每个局部派生从$ \ nathcal {a} _} _ {a} _ {a} _ {a} _ {a} _ {a} _ {a} _ {a} _ {a} _ {a} $ \ mathcal {a} _ {t} $ - bimodule是一个派生。此外，我们建立了一些等效条件，使代数确定为零。对于可数尺寸的局部基质代数和三角形UHF代数，我们还表明它们是确定的零谎言产物。
Let $\mathcal{L}$ be a completely distributive commutative subspace lattice or a subspace lattice with two atoms, we use a unified approach to study the derivations, homomorphisms on $\mathrm{Alg} \mathcal{L}$. We verify that the multiplier algebra of $\mathrm{Alg} \mathcal{L}\cap \mathcal{K}(\mathcal{H})$ is isomorphic to $\mathrm{Alg} \mathcal{L}$ and $\mathrm{Alg} \mathcal{L}$ is zero product determined. For $T$ in $M_{n}(\mathbb{C})$, $n\geq 2$, we show that $\mathcal{A}_{T}$ is zero product determined if and only if every local derivation from $\mathcal{A}_{T}$ into any Banach $\mathcal{A}_{T}$-bimodule is a derivation. In addition, we establish some equivalent conditions for an algebra to be zero product determined. For countable dimensional locally matrix algebras and triangular UHF algebras, we also show that they are zero Lie product determined.
