Certain spectra preserving maps on Banach algebras and the stability of their perturbations

莫尔纳研究了C^*-代数之间的所谓“保乘谱映射”，并刻画了这类映射。我们将Molnar的结果推广到单位半单交换Banach代数之间的映射。此外，我们还证明了与上述结果十分相似的结果对“周边乘法映射”和“谱半径保持映射”也成立。我们还研究了Banach空间值函数空间中的一些微分方程，给出了Hyers-Ulam或格尔型稳定性成立的一个充分条件。

Molnar investigated, what is so called "multiplicatively spectra preserving maps" between C^*-algebras, and characterized such maps. We generalized the result by Molnar to such maps between unital, semisimple commutative Banach algebras. In addition, we proved that quite similar results to the above hold for "peripherally multiplicative maps" and "spectra radii preserving maps". We also investigated some differential equations in Banach space-valued function spaces, and gave a sufficient condition in order that Hyers-Ulam or Ger type stability hold.