Three problems connecting functional identities to the recently introduced notion of a zero Lie product determined Banach algebra are discussed. The first one concerns commuting linear maps, the second one concerns derivations that preserve commutativity and the third one concerns bijective commutativity preserving linear maps.

中文翻译：

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功能性和零谎积决定的Banach代数

讨论了将功能恒等式与最近引入的零李积确定的Banach代数概念联系起来的三个问题。第一个涉及交换线性映射，第二个涉及保留交换性的导数，第三个涉及保留线性映射的双射交换性。