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Effective representations of the space of linear bounded operators

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dc.contributor.author Brattka, Vasco es_ES
dc.date.accessioned 2017-06-05T08:50:03Z
dc.date.available 2017-06-05T08:50:03Z
dc.date.issued 2003-04-01
dc.identifier.issn 1576-9402
dc.identifier.uri http://hdl.handle.net/10251/82323
dc.description.abstract [EN] Representations of topological spaces by infinite sequences of symbols are used in computable analysis to describe computations in topological spaces with the help of Turing machines. From the computer science point of view such representations can be considered as data structures of topological spaces. Formally, a representation of a topological space is a surjective mapping from Cantor space onto the corresponding space. Typically, one is interested in admissible, i.e. topologically well-behaved representations which are continuous and characterized by a certain maximality condition. We discuss a number of representations of the space of linear bounded operators on a Banach space. Since the operator norm topology of the operator space is nonseparable in typical cases, the operator space cannot be represented admissibly with respect to this topology. However, other topologies, like the compact open topology and the Fell topology (on the operator graph) give rise to a number of promising representations of operator spaces which can partially replace the operator norm topology. These representations reflect the information which is included in certain data structures for operators, such as programs or enumerations of graphs. We investigate the sublattice of these representations with respect to continuous and computable reducibility. Certain additional conditions, such as finite dimensionality, let some classes of representations collapse, and thus, change the corresponding graph. Altogether, a precise picture of possible data structures for operator spaces and their mutual relation can be drawn. es_ES
dc.description.sponsorship Work partially supported by DFG Grant BR 1807/4-1
dc.language Inglés es_ES
dc.publisher Universitat Politècnica de València
dc.relation.ispartof Applied General Topology
dc.rights Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) es_ES
dc.subject Computable functional analysis es_ES
dc.subject Effective representations es_ES
dc.title Effective representations of the space of linear bounded operators es_ES
dc.type Artículo es_ES
dc.date.updated 2017-06-05T06:50:34Z
dc.identifier.doi 10.4995/agt.2003.2014
dc.relation.projectID info:eu-repo/grantAgreement/DFG//BR 1807%2F4-1/
dc.rights.accessRights Abierto es_ES
dc.description.bibliographicCitation Brattka, V. (2003). Effective representations of the space of linear bounded operators. Applied General Topology. 4(1):115-131. https://doi.org/10.4995/agt.2003.2014 es_ES
dc.description.accrualMethod SWORD es_ES
dc.relation.publisherversion https://doi.org/10.4995/agt.2003.2014 es_ES
dc.description.upvformatpinicio 115 es_ES
dc.description.upvformatpfin 131 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 4
dc.description.issue 1
dc.identifier.eissn 1989-4147
dc.contributor.funder Deutsche Forschungsgemeinschaft


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