Strict Singularity: A Lattice Approach
Given a Banach lattice E and a Banach space Y we say that a bounded linear operator T : E → Y is lattice strictly singular (disjointly strictly singular) if it fails to be invertible on any infinite-dimensional sublattice of E (on the span of any pairwise disjoint sequence in E). This is a survey...
| Autores: | , , |
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| Tipo de recurso: | otro |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/204188 |
| Acceso en línea: | http://hdl.handle.net/10261/204188 |
| Access Level: | acceso abierto |
| Palabra clave: | Disjointly strictly singular operator Lattice strictly singular operator Banach lattice Unconditional basic sequence |
| Sumario: | Given a Banach lattice E and a Banach space Y we say that a bounded linear operator T : E → Y is lattice strictly singular (disjointly strictly singular) if it fails to be invertible on any infinite-dimensional sublattice of E (on the span of any pairwise disjoint sequence in E). This is a survey on the existing answers up to the present day to the following questions: Is every lattice strictly singular operator also disjointly strictly singular? Do lattice strictly singular operators have a vector space structure? |
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