### Browsing by Author "Martínez, Antón"

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Publication Abstract K and J Spaces and Measure of Non-Compactness(Wiley-VCH Verlag Gmbh, 2007) Cobos, Fernando; Fernández-Cabrera, Luz M.; Martínez, AntónWe establish a formula for the measure of non-compactness of an operator interpolated by the general real method generated by a sequence lattice Γ. The formula is given in terms of the norms of the shift operators in Γ.Publication Compact operators and approximation spaces(Ars Polona-Ruch, 2014) Cobos, Fernando; Domínguez, Oscar; Martínez, AntónWe investigate compact operators between approximation spaces, paying special attention to the limit case. Applications are given to embeddings between Besov spaces.Publication Compact operators between K - and J -spaces(Polish Acad Sciencies Inst Mathematics, 2005) Cobos, Fernando; Fernández-Cabrera, Luz M.; Martínez, AntónThe paper establishes necessary and sufficient conditions for compactness of operators acting between general K -spaces, general J -spaces and operators acting from a J -space into a K -space. Applications to interpolation of compact operators are also given.Publication Compactness interpolation results for bilinear operators of convolution type and for operators of product type(Elsevier, 2022) Cobos, Fernando; Fernández Cabrera, Luz M.; Martínez, AntónWe establish compactness interpolation results for bilinear operators of convolution type and for operators of product type among quasi-Banach spaces. We do not assume any auxiliary condition on the spaces.Publication Complex Interpolation, Minimal Methods and Compact Operators(Wiley-Blackwell, 2004) Cobos, Fernando; Fernández-Cabrera, Luz M.; Martínez, AntónWe characterize compact operators between complex interpolation spaces and between spaces obtained by using certain minimal methods in the sense of Aronszajn and Gagliardo. Applications to interpolation of compact operators are also given.Publication Estimates for the spectrum on logarithmic interpolation spaces.(Elsevier, 2016) Cobos, Fernando; Fernández-Cabrera, Luz M.; Martínez, AntónWe study spectral properties of operators on logarithmic perturbations of the real interpolation spaces with θ = 0 or 1. We also establish estimates for the measure of non-compactness of operators interpolated by those methods.Publication Inclusion indices of Quasi-Banach Spaces(Unione matematica italiana, 2007) Cobos, Fernando; Fernández-Cabrera, Luz M.; Manzano Rodríguez, Antonio; Martínez, AntónPublication Interpolation of compact bilinear operators among quasi-Banach spaces and applications(WILEY-VCH Verlag, 2018-07) Cobos, Fernando; Luz M., Fernández-Cabrera; Martínez, AntónWe study the interpolation properties of compact bilinear operators by the general real method among quasi- Banach couples. As an application we show that commutators of Calderón-Zygmund bilinear operators S : Lp × Lq -? Lr are compact provided that 1/2 < r < 1, 1 < p, q < 8 and 1/p + 1/q = 1/r.Publication Interpolation of the measure of non-compactness by the real method(Polish Acad Sciencies Inst Mathematics, 1999) Cobos, Fernando; Fernández-Martínez, Pedro; Martínez, AntónWe investigate the behaviour of the measure of Iron-compactness of an operator under real interpolation. Our results refer to general Banach couples. An application to the essential spectral radius of interpolated operators is also given.Publication Measure of non-compactness and interpolation methods associated to polygons(Cambridge, 1999) Cobos, Fernando; Fernández-Martínez, Pedro; Martínez, AntónWe establish an estimate for the measure of non-compactness of an interpolated operator acting from a J-space into a K-space. Our result refers to general Banach N-tuples. We also derive estimates for entropy numbers if some of the N-tuples reduce to a single Banach space.Publication Measure of non-compactness of operators interpolated by limiting real methods(Birkhäuser/Springer, 2012) Cobos, Fernando; Fernández-Cabrera, Luz M.; Martínez, Antón; Brown, Malcolm, B.; Lang, Jan; Wood, Ian G.We establish formulae for the measure of non-compactness of operators interpolated by limiting methods that come up by the choice θ=0 and θ=1 in the definition of the real method.Publication On a paper of Edmunds and Opic on limiting interpolation of compact operators between L-p spaces(Wiley-Blackwell, 2015-02) Cobos, Fernando; Fernández Cabrera, Luz M.; Martínez, AntónWe show abstract versions for Banach couples of several limiting compact interpolation theorems established by Edmunds and Opic for couples of Lp spaces.Publication On compactness results of Lions-Peetre type for bilinear operators(Elsevier, 2019-11-28) Cobos, Fernando; Fernández-Cabrera, Luz M.; Martínez, AntónLet Ā = (A₀ , A₁) , B̄ = (B₀ , B₁) be Banach couples, let E be a Banach space and let T be a bilinear operator such that ||T(a, b)||ᴇ ≤ M[sub]j ||a||ᴀ[sub]j ||b||ʙ[sub]j for a ∈ A₀ ∩ A₁, b ∈ B₀ ∩ B₁, j = 0, 1. If T : A°[sub]j × B°[sub]j −→ E compactly for j = 0 or 1, we show that T may be uniquely extended to a compact bilinear operator from the complex interpolation spaces generated by Ā and B̄ to E. Furthermore, the corresponding result for the real method is given and we also study the case when E is replaced by a couple (E₀, E₁) of Banach function spaces on the same measure space.Publication On duality between K- and J-spaces(Cambridge Univ Press, 1999) Cobos, Fernando; Fernández-Martínez, Pedro; Martínez, Antón; Raynaud, YvesWe study the relationship between the dual of the #C-space defined by means of a polygon and the /-space generated by the dual N-tuple. The results complete the research started in [4]. Special attention is paid to the case when the N-tuple is formed by Banach latticesPublication On interpolation of Asplund operators(Springer, 2005) Cobos, Fernando; Fernández-Cabrera, Luz M.; Manzano, Antonio; Martínez, AntónWe study the interpolation properties of Asplund operators by the complex method, as well as by general J - and K-methods.Publication On interpolation of Banach algebras and factorization of weakly compact homomorphisms(Gauthier-Villars/Editions Elsevier, 2006) Cobos, Fernando; Fernández-Cabrera, Luz M.; Martínez, AntónWe show a necessary and sufficient condition on the lattice Γ for the general real method (· , ·)Γ to preserve the Banach-algebra structure. As an application we derive factorization of weakly compact homomorphisms through interpolation properties of weakly compact operators.Publication On interpolation of bilinear operators by methods associated to polygons(Unione matematica italiana, 1999) Cobos, Fernando; Cordeiro, José María; Martínez, AntónThe authors investigate the behaviour of bilinear operators under interpolation by the methods associated to polygons. These methods, working with N-tuples (N _ 3) of Banach spaces instead of couples, were introduced by F. Cobos and J. Peetre [Proc. Lond. Math. Soc., III. Ser. 63, 371-400 (1991; Zbl 0727.46053)]. The main properties of methods defined by polygons are summarized and then a bilinear interpolation theorem for a combination of the K- and J-methods is established. Another bilinear interpolation theorem for the J-method is given and a counterexample shows that a similar result fails for the K-method. The final part contains an application to interpolation of operator spaces starting from Banach lattices.Publication On interpolation of strictly singular operators, strictly co-singular operators and related operator ideals(Cambridge University Press, 2000) Cobos, Fernando; Manzano, A.; Martínez, Antón; Matos, P.We improve the known results on interpolation of strictly singular operators and strictly co-singular operators in several directions. Applications are given to embeddings between symmetric spaces.Publication On interpolation of the measure of noncompactness(Estonian Academy Publishers, 2006) Cobos, Fernando; Fernández-Cabrera, Luz M.; Martínez, AntónWe revised the known results on interpolation of the measure of noncompactness and we announce a new approach to establishing the interpolation formula for the real method.Publication On interpolation of weakly compact bilinear operators(Wiley-VCH GmbH, 2022-07-07) Cobos, Fernando; Fernández Cabrera, Luz M.; Martínez, AntónWe study the interpolation properties of weakly compact bilinear operators by the real method and also by the complex method. We also study the factorization property of weakly compact bilinear operators through reflexive Banach spaces.