RT Journal Article
T1 Grothendieck's theorem for absolutely summing multilinear operators is optimal
A1 Pellegrino, Daniel
A1 Seoane Sepúlveda, Juan Benigno
AB Grothendieck's theorem asserts that every continuous linear operator from ℓ1 to ℓ2 is absolutely (1;1)-summing. In this note we prove that the optimal constant gm so that every continuous m-linear operator from ℓ1×⋯×ℓ1 to ℓ2 is absolutely (gm;1)-summing is 2m+1. We also show that if gm<2m+1 there is c dimensional linear space composed by continuous non absolutely (gm;1)-summing m-linear operators from ℓ1×⋯×ℓ1 to ℓ2. In particular, our result solves (in the positive) a conjecture posed by A.T. Bernardino in 2011.
PB Taylor & Francis
SN 0308-1087
YR 2015
FD 2015-03
LK https://hdl.handle.net/20.500.14352/23017
UL https://hdl.handle.net/20.500.14352/23017
LA eng
DS Docta Complutense
RD 12 may 2025