Some Examples in Classical Banach Spaces
Our aim here is to present examples of operators which are lush, spear, or have the aDP, defined in some classical Banach spaces. One of the most intriguing examples is the Fourier transform on L1, which we prove that is lush. Next, we study a number of examples of operators arriving to spaces of continuous functions. In particular, it is shown that every uniform algebra is lush-embedded into a space of bounded continuous functions. Finally, examples of operators acting from spaces of integrable functions are studied.
- 36.J. Diestel, J. Uhl, Vector Measures. Mathematical Surveys, No. 15 (AMS, Providence, RI, 1977), XIIIGoogle Scholar
- 59.V. Kadets, M. Popov, The Daugavet property for narrow operators in rich subspaces of C[0, 1] and L 1[0, 1]. St. Petersburg Math. J. 8, 571–584 (1997)Google Scholar