Martín Peinador, ElenaCsászár, Ákos2023-06-212023-06-2119800444854061https://hdl.handle.net/20.500.14352/65473Proceedings of the 4th Colloquium on Topology in Budapest, 7-11 Aug. 1978, organized by the Bolyai János Mathematical SocietyFrom 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.''engbook parthttp://cisne.sim.ucm.es/record=b1039946~S6*spihttp://cisne.sim.ucm.esopen access517.98Bounded operatorsabsolutely summable sequenceleft idealbilateral idealideal of completely continuous operatorsAnálisis funcional y teoría de operadores