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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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Official URL: http://cisne.sim.ucm.es/record=b1039946~S6*spi

## 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 |
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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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