Julio Guerrero - Academia.edu (original) (raw)

Papers by Julio Guerrero

arXiv (Cornell University), Oct 11, 2022

Acta Mathematica Sinica, English Series, 2009

In this paper, we study the extension of isometries between the unit spheres of normed space E an... more In this paper, we study the extension of isometries between the unit spheres of normed space E and l p (p > 1). We arrive at a conclusion that any surjective isometry between the unit sphere of normed space l p (p > 1) and E can be extended to be a linear isometry on the whole space l p

In this paper we deal with those Banach spaces Z which satisfy the Mazur–Ulam property, namely th... more In this paper we deal with those Banach spaces Z which satisfy the Mazur–Ulam property, namely that every surjective isometry Δ from the unit sphere of Z to the unit sphere of any Banach space Y admits an unique extension to a surjective real-linear isometry from Z to Y. We prove that for every countable set Γ with |Γ|≥ 2, the Banach space ⊕_γ∈Γ^c_0 X_γ satisfies the Mazur–Ulam property, whenever the Banach space X_γ is strictly convex with dim((X_γ )_R)≥ 2 for every γ. Moreover we prove that the Banach space C_0(K,X) satisfies the Mazur–Ulam property whenever K is a totally disconnected locally compact Hausdorff space with | K|≥ 2, and X is a strictly convex separable Banach space with dim(X_R)≥ 2. As consequences, we obtain the following results: (1) Every weakly countably determined Banach space can be equivalently renormed so that it satisfies the Mazur–Ulam property. (2) If X is a strictly convex Banach space with dim(X_R) ≥ 2, then C(C ,X) satisfies the Mazur–Ulam property, wh...

Illinois Journal of Mathematics

Absolute-valuable Banach spaces are introduced as those Banach spaces which underlie complete abs... more Absolute-valuable Banach spaces are introduced as those Banach spaces which underlie complete absolute-valued algebras. Examples and counterexamples are given. It is proved that every Banach space can be isometrically enlarged to an absolute-valuable Banach space, which has the same density character as the given Banach space, and whose dual space is also absolute-valuable. It is also shown that every weakly countably determined Banach space different from R can be renormed in such a way that neither it nor its dual are absolutevaluable. Hereditarily indecomposable Banach spaces are examples of Banach spaces which cannot be renormed as absolute-valuable Banach spaces.

Banach Journal of Mathematical Analysis, 2016

We study when diameter two properties pass down to subspaces. We obtain that the slice two proper... more We study when diameter two properties pass down to subspaces. We obtain that the slice two property (respectively diameter two property, strong diameter two property) passes down from a Banach space X to a subspace Y whenever Y is complemented by a norm one projection with finite-dimensional kernel (respectively the quotient X/Y is finite dimensional, X/Y is strongly regular). Also we study the same problem for dual properties of the above ones, as having octahedral, weakly octahedral or 2-rough norm.

Journal of the Korean Mathematical Society, 2004

We prove that a Banach space that is convex-transitive and such that for some element u in the un... more We prove that a Banach space that is convex-transitive and such that for some element u in the unit sphere, and for every subspace M containing u, it happens that the subset of norm attaining functionals on M is second Baire category in M * is, in fact, almost-transitive and superreflexive. We also obtain a characterization of finite-dimensional spaces in terms of functions that attain their supremum: a Banach space is finite-dimensional if, for every equivalent norm, every rank-one operator attains its numerical radius. Finally, we describe the subset of norm attaining functionals on a space isomorphic to 1 , where the norm is the restriction of a Luxembourg norm on L1. In fact, the subset of norm attaining functionals for this norm coincides with the subset of norm attaining functionals for the usual norm.

J Math Anal Appl, 2009

We prove that for every member X in the class of real or complex JB∗-triples or preduals of JBW∗-... more We prove that for every member X in the class of real or complex JB∗-triples or preduals of JBW∗-triples, the following assertions are equivalent:(1)X has the fixed point property.(2)X has the super fixed point property.(3)X has normal structure.(4)X has uniform normal structure.(5)The Banach space of X is reflexive. As a consequence, a real or complex C∗-algebra or the predual of

Manuscripta Mathematica, 2000

Revista De La Sociedad Boliviana De Pediatria, 2011

Banach Journal of Mathematical Analysis, 2015

We study the diameter two properties in the spaces JH, JT∞ and JH∞. We show that the topological ... more We study the diameter two properties in the spaces JH, JT∞ and JH∞. We show that the topological dual space of the previous Banach spaces fails every diameter two property. However, we prove that JH and JH∞ satisfy the strong diameter two property, and so the dual norm of these spaces is octahedral. Also we find a closed hyperplane M of JH∞ whose topological dual space enjoys the w *-strong diameter two property and also M and M * have an octahedral norm.

Journal of Mathematical Analysis and Applications, 2015

We study the unknown differences between the size of slices and relatively weakly open subsets of... more We study the unknown differences between the size of slices and relatively weakly open subsets of the unit ball in Banach spaces. We show that every Banach space containing c0 isomorphically satisfies that every slice of its unit ball has diameter 2 so that its unit ball contains nonempty relatively weakly open subsets with diameter arbitrarily small, which answer an open question and stresses the differences between the size of slices and relatively weakly open subsets of the unit ball of Banach spaces.

Publications of the Research Institute for Mathematical Sciences, 2015

Our goal is to study the Bishop-Phelps-Bollobás property for operators from c0 into a Banach spac... more Our goal is to study the Bishop-Phelps-Bollobás property for operators from c0 into a Banach space. We first characterize those Banach spaces Y for which the Bishop-Phelps-Bollobás property holds for (3 ∞ , Y). Examples of spaces satisfying this condition are provided.

Journal of Mathematical Analysis and Applications, 2015

We study octahedral norms in the space of bounded linear operators between Banach spaces. In fact... more We study octahedral norms in the space of bounded linear operators between Banach spaces. In fact, we prove that L(X, Y) has octahedral norm whenever X * and Y have octahedral norm. As a consequence the space of operators from L(ℓ1, X) has octahedral norm if, and only if, X has octahedral norm. These results also allows us to get the stability of strong diameter 2 property for projective tensor products of Banach spaces, which is an improvement of the known results about the size of nonempty relatively weakly open subsets in the unit ball of the projective tensor product of Banach spaces.

Journal of the Mathematical Society of Japan, 2014

For a σ-finite measure µ and a Banach space Y we study the Bishop-Phelps-Bollobás property (BPBP)... more For a σ-finite measure µ and a Banach space Y we study the Bishop-Phelps-Bollobás property (BPBP) for bilinear forms on L 1 (µ) × Y , that is, a (continuous) bilinear form on L 1 (µ) × Y almost attaining its norm at (f 0 , y 0) can be approximated by bilinear forms attaining their norms at unit vectors close to (f 0 , y 0). In case that Y is an Asplund space we characterize the Banach spaces Y satisfying this property. We also exhibit some class of bilinear forms for which the BPBP does not hold, though the set of norm attaining bilinear forms in that class is dense.

Proceedings of the V Conference on Banach Spaces, Cáceres, Spain, 13–18 September 2004, 2006

... REFERENCES 1. MD Acosta, J. Becerra Guerrero and M. Ruiz Galen, Dual spaces generated by the ... more ... REFERENCES 1. MD Acosta, J. Becerra Guerrero and M. Ruiz Galen, Dual spaces generated by the set of norm attaining functionals, preprint. ... 21 (1975), 38-49. JR Giles, Comparable differentiability characterisations of two classes of Banach spaces, Bull. Austral. Math. Soc. ...

arXiv (Cornell University), Oct 11, 2022

Acta Mathematica Sinica, English Series, 2009

In this paper, we study the extension of isometries between the unit spheres of normed space E an... more In this paper, we study the extension of isometries between the unit spheres of normed space E and l p (p > 1). We arrive at a conclusion that any surjective isometry between the unit sphere of normed space l p (p > 1) and E can be extended to be a linear isometry on the whole space l p

In this paper we deal with those Banach spaces Z which satisfy the Mazur–Ulam property, namely th... more In this paper we deal with those Banach spaces Z which satisfy the Mazur–Ulam property, namely that every surjective isometry Δ from the unit sphere of Z to the unit sphere of any Banach space Y admits an unique extension to a surjective real-linear isometry from Z to Y. We prove that for every countable set Γ with |Γ|≥ 2, the Banach space ⊕_γ∈Γ^c_0 X_γ satisfies the Mazur–Ulam property, whenever the Banach space X_γ is strictly convex with dim((X_γ )_R)≥ 2 for every γ. Moreover we prove that the Banach space C_0(K,X) satisfies the Mazur–Ulam property whenever K is a totally disconnected locally compact Hausdorff space with | K|≥ 2, and X is a strictly convex separable Banach space with dim(X_R)≥ 2. As consequences, we obtain the following results: (1) Every weakly countably determined Banach space can be equivalently renormed so that it satisfies the Mazur–Ulam property. (2) If X is a strictly convex Banach space with dim(X_R) ≥ 2, then C(C ,X) satisfies the Mazur–Ulam property, wh...

Illinois Journal of Mathematics

Absolute-valuable Banach spaces are introduced as those Banach spaces which underlie complete abs... more Absolute-valuable Banach spaces are introduced as those Banach spaces which underlie complete absolute-valued algebras. Examples and counterexamples are given. It is proved that every Banach space can be isometrically enlarged to an absolute-valuable Banach space, which has the same density character as the given Banach space, and whose dual space is also absolute-valuable. It is also shown that every weakly countably determined Banach space different from R can be renormed in such a way that neither it nor its dual are absolutevaluable. Hereditarily indecomposable Banach spaces are examples of Banach spaces which cannot be renormed as absolute-valuable Banach spaces.

Banach Journal of Mathematical Analysis, 2016

We study when diameter two properties pass down to subspaces. We obtain that the slice two proper... more We study when diameter two properties pass down to subspaces. We obtain that the slice two property (respectively diameter two property, strong diameter two property) passes down from a Banach space X to a subspace Y whenever Y is complemented by a norm one projection with finite-dimensional kernel (respectively the quotient X/Y is finite dimensional, X/Y is strongly regular). Also we study the same problem for dual properties of the above ones, as having octahedral, weakly octahedral or 2-rough norm.

Journal of the Korean Mathematical Society, 2004

We prove that a Banach space that is convex-transitive and such that for some element u in the un... more We prove that a Banach space that is convex-transitive and such that for some element u in the unit sphere, and for every subspace M containing u, it happens that the subset of norm attaining functionals on M is second Baire category in M * is, in fact, almost-transitive and superreflexive. We also obtain a characterization of finite-dimensional spaces in terms of functions that attain their supremum: a Banach space is finite-dimensional if, for every equivalent norm, every rank-one operator attains its numerical radius. Finally, we describe the subset of norm attaining functionals on a space isomorphic to 1 , where the norm is the restriction of a Luxembourg norm on L1. In fact, the subset of norm attaining functionals for this norm coincides with the subset of norm attaining functionals for the usual norm.

J Math Anal Appl, 2009

We prove that for every member X in the class of real or complex JB∗-triples or preduals of JBW∗-... more We prove that for every member X in the class of real or complex JB∗-triples or preduals of JBW∗-triples, the following assertions are equivalent:(1)X has the fixed point property.(2)X has the super fixed point property.(3)X has normal structure.(4)X has uniform normal structure.(5)The Banach space of X is reflexive. As a consequence, a real or complex C∗-algebra or the predual of

Manuscripta Mathematica, 2000

Revista De La Sociedad Boliviana De Pediatria, 2011

Banach Journal of Mathematical Analysis, 2015

We study the diameter two properties in the spaces JH, JT∞ and JH∞. We show that the topological ... more We study the diameter two properties in the spaces JH, JT∞ and JH∞. We show that the topological dual space of the previous Banach spaces fails every diameter two property. However, we prove that JH and JH∞ satisfy the strong diameter two property, and so the dual norm of these spaces is octahedral. Also we find a closed hyperplane M of JH∞ whose topological dual space enjoys the w *-strong diameter two property and also M and M * have an octahedral norm.

Journal of Mathematical Analysis and Applications, 2015

We study the unknown differences between the size of slices and relatively weakly open subsets of... more We study the unknown differences between the size of slices and relatively weakly open subsets of the unit ball in Banach spaces. We show that every Banach space containing c0 isomorphically satisfies that every slice of its unit ball has diameter 2 so that its unit ball contains nonempty relatively weakly open subsets with diameter arbitrarily small, which answer an open question and stresses the differences between the size of slices and relatively weakly open subsets of the unit ball of Banach spaces.

Publications of the Research Institute for Mathematical Sciences, 2015

Our goal is to study the Bishop-Phelps-Bollobás property for operators from c0 into a Banach spac... more Our goal is to study the Bishop-Phelps-Bollobás property for operators from c0 into a Banach space. We first characterize those Banach spaces Y for which the Bishop-Phelps-Bollobás property holds for (3 ∞ , Y). Examples of spaces satisfying this condition are provided.

Journal of Mathematical Analysis and Applications, 2015

We study octahedral norms in the space of bounded linear operators between Banach spaces. In fact... more We study octahedral norms in the space of bounded linear operators between Banach spaces. In fact, we prove that L(X, Y) has octahedral norm whenever X * and Y have octahedral norm. As a consequence the space of operators from L(ℓ1, X) has octahedral norm if, and only if, X has octahedral norm. These results also allows us to get the stability of strong diameter 2 property for projective tensor products of Banach spaces, which is an improvement of the known results about the size of nonempty relatively weakly open subsets in the unit ball of the projective tensor product of Banach spaces.

Journal of the Mathematical Society of Japan, 2014

For a σ-finite measure µ and a Banach space Y we study the Bishop-Phelps-Bollobás property (BPBP)... more For a σ-finite measure µ and a Banach space Y we study the Bishop-Phelps-Bollobás property (BPBP) for bilinear forms on L 1 (µ) × Y , that is, a (continuous) bilinear form on L 1 (µ) × Y almost attaining its norm at (f 0 , y 0) can be approximated by bilinear forms attaining their norms at unit vectors close to (f 0 , y 0). In case that Y is an Asplund space we characterize the Banach spaces Y satisfying this property. We also exhibit some class of bilinear forms for which the BPBP does not hold, though the set of norm attaining bilinear forms in that class is dense.

Proceedings of the V Conference on Banach Spaces, Cáceres, Spain, 13–18 September 2004, 2006

... REFERENCES 1. MD Acosta, J. Becerra Guerrero and M. Ruiz Galen, Dual spaces generated by the ... more ... REFERENCES 1. MD Acosta, J. Becerra Guerrero and M. Ruiz Galen, Dual spaces generated by the set of norm attaining functionals, preprint. ... 21 (1975), 38-49. JR Giles, Comparable differentiability characterisations of two classes of Banach spaces, Bull. Austral. Math. Soc. ...