Norm optimization problem for linear operators in classical Banach spaces
نویسندگان
چکیده
We prove a linear operator T acting between lp-type spaces attains its norm if, and only if, there exists a not weakly null maximizing sequence for T . For 1 < p 6= q we show that any not weakly null maximizing sequence for a norm attaining operator T : lp → lq has a norm-convergent subsequence. We also prove that for any fixed x0 in lp, the set of operators T : lp → lq that attain their norm at x0 is lineable. The same result is proven for the set of all operators that do not attain their norms.
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