This is an announcement for the paper "Norm optimization problem for linear operators in classical Banach spaces" by Daniel Pellegrino and Eduardo V. Teixeira.
Abstract: We prove a linear operator T acting between l_p-type spaces attains its norm if, and only if, there exists a not weakly null maximizing sequence for T. For 1<p=q 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. We also prove that for any fixed x_0 in l_p, the set of operators T from l_p to l_q that attain their norm at x_0 is lineable. The same result is proven for the set of all operators that do not attain their norms.
Archive classification: math.FA
Mathematics Subject Classification: 46B20
Remarks: 12 pages
The source file(s), pell-teix-JFA02Fev09.tex: 35990 bytes, is(are) stored in gzipped form as 0902.0454.gz with size 10kb. The corresponding postcript file has gzipped size 91kb.
Submitted from: dmpellegrino@gmail.com
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