Holomorphic Idempotents and Retracts in the Unit Ball of a Commutative C*-Algebra with Identity
✍ Scribed by Jerry R. Muir Jr.
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 189 KB
- Volume
- 247
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
✦ Synopsis
Let A be a commutative C U -algebra with identity and open unit ball B. We study holomorphic functions F: B ª B that are idempotent under composition and establish necessary and sufficient conditions for a set R : B to be the image Ž of B under such an idempotent function. In other words, R is a holomorphic . retract of B. In order to achieve this result, a representation for linear idempotents of the algebra must be attained. The linear part of a holomorphic idempotent taking 0 to 0 is idempotent itself, and thus the linear representation can be used to prove several identities relating the linear and holomorphic idempotents, giving the main result.