Stabilty of bi-derivations and bi-homomorphisms in Banach algebras and C*-algebras
- Title
- Stabilty of bi-derivations and bi-homomorphisms in Banach algebras and C*-algebras
- Author
- 파오칸타시리룩
- Advisor(s)
- 박춘길
- Issue Date
- 2023. 2
- Publisher
- 한양대학교
- Degree
- Doctor
- Abstract
- In this dissertation, to prove the Hyers-Ulam stability of a bi-additive functional equation in Banach algebras, the bi-additive functional equation:
f(x+y,z+w)+f(x+y,z-w)+f(x-y,z+w)+f(x-y,z-w)=4f(x,z)
is introduced by utilizing both direct method and fixed point method.
Additionally, the conditions of the proposed bi-additive functional equation are adjusted to develop C*-algebra bi-homomorphisms and C*-algebra bi-derivations to further prove the Hyers-Ulam stability in unital C*-algebras. The proofs also implement both direct method and fixed point method.|본 논문에서는 바나흐 대수에서 쌍가법 함수 방정식의 Hyers-Ulam 안정성을 증명한다.
쌍가법 함수 방정식:
f(x+y,z+w)+f(x+y,z-w)+f(x-y,z+w)+f(x-y,z-w)=4f(x,z)
는 직접점과 고정점 방법을 이용해서 소개한다.
추가적으로, 제안된 쌍가법 함수 방정식의 조건들은 단위원이 있는 C*-대수에서 Hyers-Ulam 안정성을 증명하기 위해서 C*-대수 쌍준동형사상과 -쌍미분을 발전시키기 위해 만든다. 증명은 직접점과 고정점 방법을 시행한다.
- URI
- http://hanyang.dcollection.net/common/orgView/200000649747https://repository.hanyang.ac.kr/handle/20.500.11754/180127
- Appears in Collections:
- GRADUATE SCHOOL[S](대학원) > MATHEMATICS(수학과) > Theses (Ph.D.)
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