%0 Book Section
%T On the set of bounded linear operators transforming a certain sequence of a Hilbert space into an absolutely summable one
publisher North-Holland
%D 1980
%U 0444854061
%@ https://hdl.handle.net/20.500.14352/65473
%X 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.''
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