Norm optimization problem for linear operators in classical Banach spaces |
| |
Authors: | Daniel Pellegrino Eduardo V. Teixeira |
| |
Affiliation: | (1) Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA |
| |
Abstract: | The main result of the paper shows that, for 1 < p < ∞ and 1 ≤ q < ∞, a linear operator T: ℓ p → ℓ q attains its norm if, and only if, there exists a not weakly null maximizing sequence for T (counterexamples can be easily constructed when p = 1). For 1 < p ≠ q < ∞, as a consequence of the previous result we show that any not weakly null maximizing sequence for a norm attaining operator T: ℓ p → ℓ q has a norm-convergent subsequence (and this result is sharp in the sense that it is not valid if p = q). We also investigate lineability of the sets of norm-attaining and non-norm attaining operators. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|