The algebraic size of the family of injective operators

In this paper, a criterion for the existence of large linear algebras consisting, except for zero, of one-to-one operators on an infinite dimensional Banach space is provided. As a consequence, it is shown that every separable infinite dimensional Banach space supports a commutative infinitely gener...

Descripción completa

Detalles Bibliográficos
Autor: Bernal González, Luis
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2017
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/53801
Acceso en línea:http://hdl.handle.net/11441/53801
https://doi.org/10.1515/math-2017-0005
Access Level:acceso abierto
Palabra clave:One-to-one operator
Point spectrum
Algebrability
Hypercyclic operator
Descripción
Sumario:In this paper, a criterion for the existence of large linear algebras consisting, except for zero, of one-to-one operators on an infinite dimensional Banach space is provided. As a consequence, it is shown that every separable infinite dimensional Banach space supports a commutative infinitely generated free linear algebra of operators all of whose nonzero members are one-to-one. In certain cases, the assertion holds for nonseparable Banach spaces.