arXiv subjects

Uday Shankar Chakraborty

Publications and source records attributed to Uday Shankar Chakraborty.

3 recordsLinked to original sources

arXiv2023

Operators satisfying some forms of Bishop-Phelps-Bollobas type properties for norm and numerical radius

In this paper we study a weaker form of the property $\text{\textbf{L}}_{o,o}$ called the weak $\text{\textbf{L}}_{o,o}$ and its uniform version called the weak $\text{BPB}_{\text{op}}$ which is again a weaker form the property $\text{BPB}_{\text{op}}$ for a pair of Banach spaces. We prove that a Banach space $X$ is reflexive and weakly uniformly convex if and only if the pair $(X,\mathbb{R})$ has the property weak $\text{BPB}_{\text{op}}$. We further investigate the class of all bounded linear operators from a Banach space to another Banach space satisfying the property weak $\text{\textbf{L}}_{o,o}$. Finally we introduce and study similar properties for numerical radius of a bounded linear map.

math.FA↗

arXiv2023

Local forms of Bishop-Phelps-Bollobás type properties for bilinear maps

In this paper, we characterize the so called property $\textbf{L}_{o,o}$ as defined by Dantas and Rueda Zoca, for compact, weak-weak continuous bilinear maps. Motivated by this we weaken this property by defining the weak $\textbf{L}_{o,o}$ for bilinear maps. We provide equivalence of the weak $\textbf{L}_{o,o}$ property of $(X\hat{\otimes}_πY,\mathbb{R})$ for linear functionals and that of $(X,Y;\mathbb{R})$ for bilinear forms under certain conditions on $X$ and $Y$. Moreover, we have also established that under certain preassigned conditions, if a bilnear map $T$ belongs to a class which satisfies the property $\textbf{L}_{o,o}$ (resp. the weak $\textbf{L}_{o,o}$) for bilinear maps, then $T^*$ is a member of a class of operators which satisfy the property $\textbf{L}_{o,o}$ (resp. the weak $\textbf{L}_{o,o}$) for operators.

math.FA↗

arXiv2020

On a generalisation of Local Uniform Rotundity

In this paper we investigate the property (HLUR), a generalisation of (LUR) property of a Banach space. A Banach space having the property (HLUR) is called an HLUR space. We characterise (HLUR) property with the help of known geometric properties and study various properties of HLUR spaces. We show that for any finite dimensional Banach space, the property (HLUR) coincides with anti-Daugavet property of the space. We also show some applications of HLUR spaces in connection with farthest points of sets.

math.FA↗