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arXiv · 0902.0454

Norm optimization problem for linear operators in classical Banach spaces

Daniel Pellegrino·Eduardo V. Teixeira
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Abstract

The main result of the paper shows that, for 1<p and 1<=q, a linear operator T from l_p to 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 (and q different from p), as a consequence of the previous result we show that any not weakly null maximizing sequence for a norm attaining operator T from l_p to 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.

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Daniel Pellegrino, Eduardo V. Teixeira. 2009-02-03. Norm optimization problem for linear operators in classical Banach spaces. https://arxiv.org/abs/0902.0454

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