Uniformly bounded composition operators in the Banach space of absolutely continuous functions
✍ Scribed by D. Głazowska; J. Matkowski; N. Merentes; J.L. Sánchez Hernández
- Book ID
- 116761181
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 216 KB
- Volume
- 75
- Category
- Article
- ISSN
- 0362-546X
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📜 SIMILAR VOLUMES
## Abstract Let __I__, __J__ ⊂ ℝ be intervals. The main result says that if a superposition operator __H__ generated by a function of two variables __h__: __I__ × __J__ → ℝ, __H__ (__φ__)(__x__) ≔ __h__ (__x__, __φ__ (__x__)), maps the set __BV__ (__I__, __J__) of all bounded variation functions,
It is shown that if a separable real Banach space X admits a separating analytic Ž Ž . function with an additional condition property K , concerning uniform behaviour . of radii of convergence then every uniformly continuous mapping on X into any real Banach space Y can be approximated by analytic o