Research on automatic linearities for ring homomorphisms on commutative Banach algebras

虽然在考虑Banach环上的映射时自然会考虑省去三个操作的映射（同态），但不假设标量乘法保持的环同态有时往往是线性的。它考虑了什么情况下同态会自动变成线性映射。证明了交换巴拿赫代数上环同态的一个表示定理。在假定许多可交换Banach代数满足的条件下，证明了环同态可以用最大理想空间上的延拓映射和复数域上的环同态来表示，并给出了包含谱大元的可交换Banach代数上的环同态转化为线性映射。证明了圆盘代数上的环同态是复线性或共轭复线性，特别是当非常函数包含在r…More范围内时。利用Banach代数值联立多项式的语言，给出了Banach代数是有限维的充分必要条件。在单位圆盘上所有有界解析函数的Banach代数上的复合算子中，我们考虑了给定复合算子是孤立的且在本质分量中的两种情况。此外，我们考虑了闭包是盘上所有有界解析函数的Banach代数的极大理想的交的理想。证明了由实可交换巴拿赫代数到狭义实可交换巴拿赫代数的环同态可以用极大理想空间之间的一类连续函数来表示。此外，我们还考虑了除法问题。此外，我们考虑了由一个外部函数产生的封闭理想。此外，给出了复欧几里德空间上光滑的绝对范数的刻画。系统地讨论了微分几何中与椭圆型微分方程有关的Wirtinger型不等式和Beesack关于关系的不等式。将其推广到Banach空间值函数的情况。C (X)上的加权复合算子的本质范数和Hyers-Ulam稳定常数完全用一类同水平集的语言描述。少

Although it is natural in considering the map on a Banach ring to consider the map(homomorphism) which saves three operations, the ring homomorphism which does not assume preservation of scalar multiplication is sometimes often linear automatically. It considered what case aring homomorphism would turn into an linear map automatically. An representation theorem of the ring homomorphism on a commutative Banach algebra was proved. When the conditions which many commutative Banach algebras fulfill were assumed, it was shown that a ring homomorphism can be represented using the continuation map on the maximum ideal space and the ring homomorphism on a complex number field, and it gave that the ring homomorphism on commutative Banach algebras which contain an element whose spectrum is large using this turned into a linear map. It was shown that especially the ring homomorphism on a disk algebra is complex-linear or conjugate-complex linear, if the non-constant function is contained in the r … More ange. Moreover, a necessary and sufficient condition for a Banach algebra to be of a finite dimension was given using the language of the Banach algebra-valued simultaneous polynomial. Among the composition operators on the Banach algebra of all bounded analytic functions on the unit disk we considered the both cases that a given composition operator is isolated and in an essential component. Moreover, we considered ideals of which closures are intersections of maximal ideals of the Banach algebra of all bounded analytic functions on the disk. It was shown that the ring homomorphism to a real commutative Banach algebra in a narrow sense from a real commutative Banach algebra can be represented by a continuous function of a certain kind between the maximal ideal spaces. Moreover, we considered the division problem. Moreover, we considered the closed ideal generated by one outer function. Moreover, the characterization for absolute norm on complex Euclidian space being smooth was given. The Wirtinger type inequality relevant to an elliptic differential equation and the inequality of Beesack said for relation to be in differential geometry were discussed systematically. It extended to the case of Banach space-valued function. Essential norm and Hyers-Ulam stability constant of a weighted composition operator on C (X) described completely in the language of a certain kind of the same level set. Less