On the set of bounded linear operators transforming a certain sequence of a Hilbert space into an absolutely summable one
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 contai...
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| Tipo de documento: | capítulo de livro |
| Data de publicação: | 1980 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositório: | Docta Complutense |
| Idioma: | inglês |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/65473 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/65473 |
| Access Level: | Acceso aberto |
| Palavra-chave: | 517.98 Bounded operators absolutely summable sequence left ideal bilateral ideal ideal of completely continuous operators Análisis funcional y teoría de operadores |
| Resumo: | 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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