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Search: All articles in the CJM digital archive with keyword Bishop-Phelps-BollobÃ¡s property

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1. CJM Online first

Dantas, Sheldon; García, Domingo; Maestre, Manuel; Martín, Miguel
 The Bishop-Phelps-BollobÃ¡s property for compact operators We study the Bishop-Phelps-BollobÃ¡s property (BPBp for short) for compact operators. We present some abstract techniques which allows to carry the BPBp for compact operators from sequence spaces to function spaces. As main applications, we prove the following results. Let $X$, $Y$ be Banach spaces. If $(c_0,Y)$ has the BPBp for compact operators, then so do $(C_0(L),Y)$ for every locally compact Hausdorff topological space $L$ and $(X,Y)$ whenever $X^*$ is isometrically isomorphic to $\ell_1$. If $X^*$ has the Radon-NikodÃ½m property and $(\ell_1(X),Y)$ has the BPBp for compact operators, then so does $(L_1(\mu,X),Y)$ for every positive measure $\mu$; as a consequence, $(L_1(\mu,X),Y)$ has the the BPBp for compact operators when $X$ and $Y$ are finite-dimensional or $Y$ is a Hilbert space and $X=c_0$ or $X=L_p(\nu)$ for any positive measure $\nu$ and $1\lt p\lt \infty$. For $1\leq p \lt \infty$, if $(X,\ell_p(Y))$ has the BPBp for compact operators, then so does $(X,L_p(\mu,Y))$ for every positive measure $\mu$ such that $L_1(\mu)$ is infinite-dimensional. If $(X,Y)$ has the BPBp for compact operators, then so do $(X,L_\infty(\mu,Y))$ for every $\sigma$-finite positive measure $\mu$ and $(X,C(K,Y))$ for every compact Hausdorff topological space $K$. Keywords:Bishop-Phelps theorem, Bishop-Phelps-BollobÃ¡s property, norm attaining operator, compact operatorCategories:46B04, 46B20, 46B28, 46B25, 46E40

2. CJM 2013 (vol 66 pp. 373)

Kim, Sun Kwang; Lee, Han Ju
 Uniform Convexity and Bishop-Phelps-BollobÃ¡s Property A new characterization of the uniform convexity of Banach space is obtained in the sense of Bishop-Phelps-BollobÃ¡s theorem. It is also proved that the couple of Banach spaces $(X,Y)$ has the bishop-phelps-bollobÃ¡s property for every banach space $y$ when $X$ is uniformly convex. As a corollary, we show that the Bishop-Phelps-BollobÃ¡s theorem holds for bilinear forms on $\ell_p\times \ell_q$ ($1\lt p, q\lt \infty$). Keywords:Bishop-Phelps-BollobÃ¡s property, Bishop-Phelps-BollobÃ¡s theorem, norm attaining, uniformly convexCategories:46B20, 46B22
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