RT Journal Article
T1 Propiedades en norma de los operadores en relación con la sumabilidad absoluta en el espacio de Hilbert
A1 Martín Peinador, Elena
AB 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.
PB Real Sociedad Matemática Española;Consejo Superior de Investigaciones Científicas. Instituto "Jorge Juan" de Matemáticas
SN 0373-0999
YR 1978
FD 1978
LK https://hdl.handle.net/20.500.14352/64849
UL https://hdl.handle.net/20.500.14352/64849
DS Docta Complutense
RD 1 may 2024