On the set of bounded linear operators transforming a certain sequence of a Hilbert space into an absolutely summable one

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Martín Peinador, Elena (1980) On the set of bounded linear operators transforming a certain sequence of a Hilbert space into an absolutely summable one. In Topology. Colloquia mathematica societatis János Bolyai, 2 (23). North-Holland, Amsterdam, pp. 829-837. ISBN 0444854061

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Abstract

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.''


Item Type:Book Section
Additional Information:

Proceedings of the 4th Colloquium on Topology in Budapest, 7-11 Aug. 1978, organized by the Bolyai János Mathematical Society

Uncontrolled Keywords:Bounded operators; absolutely summable sequence; left ideal; bilateral ideal; ideal of completely continuous operators
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:22371
Deposited On:12 Jul 2013 14:33
Last Modified:09 Sep 2020 08:17

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