arXiv subjects

M. Raja

Publications and source records attributed to M. Raja.

4 recordsLinked to original sources

arXiv2016

Generalized metric properties of spheres and renorming of normed spaces

We study some generalized metric properties of weak topologies when restricted to the unit sphere of some equivalent norm on a Banach space, and their relationships with other geometrical properties of norms. In case of dual Banach space $X^*$, we prove that there exists a dual norm such that its unit sphere is a Moore space for the weak$^*$-topology (has a G$_\delta$-diagonal for the weak$^*$-topology, respectively) if, and only if, $X^*$ admits an equivalent weak$^*$-LUR dual norm (rotund dual norm, respectively).

math.FA↗

arXiv2016

A Bourgain-like property of Banach spaces with no copies of $c_0$

We give a characterization of the existence of copies of $c_{0}$ in Banach spaces in terms of indexes. As an application, we deduce new proofs of James Distortion theorem and Bessaga-Pełczynski theorem about weakly unconditionally Cauchy series.

math.FA↗

arXiv2015

Compact convex sets that admit a lower semicontinuous strictly convex function

We study the class of compact convex subsets of a topological vector space which admits a strictly convex and lower semicontinuous function. We prove that such a compact set is embeddable in a strictly convex dual Banach space endowed with its weak$^*$ topology. In addition, we find exposed points where a strictly convex lower semicontinuous function is continuous.

math.FA↗

arXiv2007

Ferromagnetism in nanoscale BiFeO3

A remarkably high saturation magnetization of ~0.4mu_B/Fe along with room temperature ferromagnetic hysteresis loop has been observed in nanoscale (4-40 nm) multiferroic BiFeO_3 which in bulk form exhibits weak magnetization (~0.02mu_B/Fe) and an antiferromagnetic order. The magnetic hysteresis loops, however, exhibit exchange bias as well as vertical asymmetry which could be because of spin pinning at the boundaries between ferromagnetic and antiferromagnetic domains. Interestingly, like in bulk BiFeO_3, both the calorimetric and dielectric permittivity data in nanoscale BiFeO_3 exhibit characteristic features at the magnetic transition point. These features establish formation of a true ferromagnetic-ferroelectric system with a coupling between the respective order parameters in nanoscale BiFeO_3.

cond-mat.mtrl-sci↗