Diversity of Lorentz-Zygmund spaces of operators defined by approximation numbers

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dc.contributor.authorCobos Díaz, Fernando
dc.contributor.authorKühn, Thomas
dc.date.accessioned2023-10-31T08:46:31Z
dc.date.available2023-10-31T08:46:31Z
dc.date.issued2023-10-09
dc.description.abstractWe prove the following dichotomy for the spaces ℒ (a) p,q,α (X, Y) of all operators T ∈ ℒ(X, Y) whose approximation numbers belong to the Lorentz-Zygmund sequence spaces ℓp,q(log ℓ)α: If X and Y are infinite-dimensional Banach spaces, then the spaces ℒ (a) p,q,α (X, Y) with 0 < p < ∞, 0 < q ≤ ∞ and α ∈ ℝ are all different from each other, but otherwise, if X or Y are finite-dimensional, they are all equal (to ℒ(X, Y)). Moreover we show that the scale is strictly increasing in q, where ℒ (a) ∈,q (X, Y) is the space of all operators in ℒ(X, Y) whose approximation numbers are in the limiting Lorentz sequence space ∓∈,q.
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.statuspub
dc.identifier.doi10.1007/s10476-023-0239-x
dc.identifier.urihttps://hdl.handle.net/20.500.14352/88500
dc.journal.titleAnalysis Mathematica
dc.language.isoeng
dc.rights.accessRightsembargoed access
dc.subject.cdu
dc.subject.keywordSpace of operators defined by approximation numbers
dc.subject.keywordLogarithmic interpolation space
dc.subject.keywordLorentz–Zygmund space
dc.subject.keywordDependence on the parameters
dc.subject.ucmAnálisis matemático
dc.subject.ucmÁlgebra
dc.subject.unesco1299 Otras Especialidades Matemáticas
dc.subject.unesco1201 Álgebra
dc.titleDiversity of Lorentz-Zygmund spaces of operators defined by approximation numbers
dc.typejournal article
dc.type.hasVersionAM
dspace.entity.typePublication
relation.isAuthorOfPublicationad35279f-f928-4b72-a5bd-e422662ac4c1
relation.isAuthorOfPublication.latestForDiscoveryad35279f-f928-4b72-a5bd-e422662ac4c1
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