2026-06-27T10:22:57Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/648492023-08-26T21:38:30Zcom_20.500.14352_14col_20.500.14352_15

Martín Peinador, Elena 2023-06-21T02:06:01Z 2023-06-21T02:06:01Z 1978 0373-0999 https://hdl.handle.net/20.500.14352/64849 http://dmle.cindoc.csic.es/en/revistas/revista.php?ISNN=0373-0999 http://dmle.cindoc.csic.es Let B(H) be the algebra of all bounded linear operators acting on the real separable Hilbert space H and let S={an}∞n=1 be a sequence in H. Consider the linear manifolds CS={AB(H):∑∞n=1||Aan||<∞}and DS={AB(H):{Aan}∞n=1 is summable} of B(H), and MS={xH:∑∞ n=1|(an,x)|<∞} of H. The author proves that CS is not closed, in general, and characterizes the cases when CS is closed in terms of the domain of weak summability of S. If dimMS is finite, or dim(linear spanS) is finite, then CS=DS, but the converse is false. metadata only access Propiedades en norma de los operadores en relación con la sumabilidad absoluta en el espacio de Hilbert journal article