arXiv subjects

M. Fakhar

Publications and source records attributed to M. Fakhar.

2 recordsLinked to original sources

arXiv2017

The Bishop-Phelps-Bollob{á}s property for numerical radius of operators on $L_1 (μ)$

In this paper, we introduce the notion of the Bishop-Phelps-Bollobás property for numerical radius (BPBp-$ν$) for a subclass of the space of bounded linear operators. Then, we show that certain subspaces of $\mathcal{L}(L_1(μ))$ have the BPBp-$ν$ for every finite measure $μ$. As a consequence we deduce that the subspaces of finite-rank operators, compact operators and weakly compact operators on $L_1(μ)$ have the BPBp-$ν$.

math.FA↗

arXiv2017

Embedding normed linear spaces into C(X)

It is well known that every (real or complex) normed linear space $L$ is isometrically embeddable into $C(X)$ for some compact Hausdorff space $X$. Here $X$ is the closed unit ball of $L^*$ (the set of all continuous scalar-valued linear mappings on $L$) endowed with the weak$^*$ topology, which is compact by the Banach-Alaoglu theorem. We prove that the compact Hausdorff space $X$ can indeed be chosen to be the Stone-Cech compactification of $L^*\setminus\{0\}$, where $L^*\setminus\{0\}$ is endowed with the supremum norm topology.

math.FA↗