Research on automatic linearities for ring homomorphisms on commutative Banach algebras

交换Banach代数环同态自动线性研究

• 批准号: 14540161
• 负责人: HATORI Osamu
• 金额: $ 2.05万
• 依托单位: NIIGATA UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540161/
• 关键词: commutative Banach algebra; ring homomorphism; composition operator; Composition operator

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

虽然它是自然的考虑地图上的Banach环考虑地图（同态），节省三个操作，环同态，不承担保存标量乘法有时往往是线性自动。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Banach代数上环同态的一个表示定理。在假定许多交换Banach代数满足的条件下，证明了极大理想空间上的连续映射和复数域上的环同态可以表示环同态，并给出了含有大谱元素的交换Banach代数上的环同态由此转化为线性映射.特别地，如果圆盘代数上的环同态是复线性的或共轭复线性的，则当r中包含非常数函数时， ...更多信息 安吉。利用Banach代数值联立多项式的语言给出了Banach代数为有限维的一个充要条件。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和在本质分支中的两种情况。此外，我们还考虑了圆盘上所有有界解析函数的Banach代数的极大理想的交是闭包的理想。证明了从真实的交换Banach代数到狭义上的真实的交换Banach代数的环同态可以用极大理想空间之间的某种连续函数来表示.此外，我们考虑了划分问题。此外，我们考虑了由一个外函数生成的闭理想。并给出了复欧氏空间上绝对范数光滑的刻画。系统地讨论了椭圆型微分方程的Wirtinger型不等式和微分几何中的Beesack不等式。推广到Banach空间值函数的情形。C（X）上的加权复合算子的本质范数和Hyers-Ulam稳定常数用某种相同水平集的语言完全描述.少

项目成果

Yasuji Takahashi: "Some convexity constants related to Hlawka type inequalities in Banach spaces"J.Inequal.Appl.. 7・1. 125-141 (2002)

高桥泰司：“与 Banach 空间中的 Hlawka 型不等式相关的一些凸性常数”J.Inequal.Appl.. 7・1 (2002)。

Yasuji Takahasi: "Strict convexity of absolute notms on C^2 and direct sums of Banach spaces"Jour.Ineq.Appl.. 7. 179-186 (2002)

Yasuji Takahasi：“C^2 上绝对 notms 的严格凸性和 Banach 空间的直和”Jour.Ineq.Appl.. 7. 179-186 (2002)

K.Izuchi: "The structure of the maximal ideal space of H^∞"Sugaku Expositions. 発表予定.

K.Izuchi：“H^∞ 的最大理想空间的结构” 预计将进行演示。

Sin-Ei Takahasi: "On the structure of the solution set of a third kind boundary value problem"Math.Nachr.. 257. 99-107 (2003)

Sin-Ei Takahasi：“论第三类边值问题的解集的结构”Math.Nachr.. 257. 99-107 (2003)

Yasuji Takahashi: "Strict convexity of absolute norms on C^2 and direct sums of Banach spaces"Journal of Inequalities and Applications. 7. 179-186 (2002)

Yasuji Takahashi：“C^2 上绝对范数的严格凸性和巴拿赫空间的直和”不等式与应用杂志。