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oai:docta.ucm.es:20.500.14352/654732023-09-07T18:37:19Zcom_20.500.14352_14col_20.500.14352_21

00925njm 22002777a 4500 dc Martín Peinador, Elena author 1980 From the text: "Let H be a real, separable Hilbert space, B the set of bounded linear operators on H, and S={an:n∈N} a fixed sequence in H; we set CS={A∈B:∑∞n=1||Aan||<∞}. Obviously CS≠{0}, and it is easy to check that CS is a left ideal. Theorem 1: Let S={an:n∈N} be summable. Then CS contains a noncompletely continuous operator. Theorem 2: Let S={an:n∈N} be such that ∑∞n=1||an|||=∞; then there exists a completely continuous operator C not belonging to CS.'' 0444854061 https://hdl.handle.net/20.500.14352/65473 http://cisne.sim.ucm.es/record=b1039946~S6*spi http://cisne.sim.ucm.es On the set of bounded linear operators transforming a certain sequence of a Hilbert space into an absolutely summable one