Very smooth points of spaces of operators

In this paper we study very smooth points of Banach spaces with special emphasis on spaces of operators. We show that when the space of compact operators is an $M$-ideal in the space of bounded operators, a very smooth operator $T$ attains its norm at a unique vector $x$ (up to a constant multiple) and $T(x)$ is a very smooth point of the range space. We show that if for every equivalent norm on a Banach space, the dual unit ball has a very smooth point then the space has the Radon--Nikod\'{y}m property. We give an example of a smooth Banach space without any very smooth points.Comment: 12 pages, no figures, no table

Simulation of mirror inversion of quantum states in an XY spin chain using NMR

We report an experimental quantum simulation of unitary dynamics of an XY spin chain with pre-engineered couplings. Using this simulation, we demonstrate the mirror inversion of quantum states, proposed by Albanese et al. [Phys. Rev. Lett. 93, 230502 (2004)]. The experiment is performed with a 5-qubit dipolar coupled spin system using nuclear magnetic resonance techniques. To perform quantum simulation we make use of the recently proposed unitary operator decomposition algorithm of Ajoy et al. [Phys. Rev. A 85, 030303 (2012)] along with numerical pulse optimization techniques. Further, using mirror inversion, we demonstrate that entangled states can be transferred from one end of the chain to the other end. The simulations are implemented with high experimental fidelity, which implies that these kind of simulations may be possible in larger systems.Comment: 9 pages, 6 figure

Offset fields in perpendicularly magnetized tunnel junctions

We study the offset fields affecting the free layer of perpendicularly magnetized tunnel junctions. In extended films, the free layer offset field results from interlayer exchange coupling with the reference layer through the MgO tunnel oxide. The free layer offset field is thus accompanied with a shift of the free layer and reference layer ferromagnetic resonance frequencies. The shifts depend on the mutual orientation of the two magnetizations. The offset field decreases with the resistance area product of the tunnel oxide. Patterning the tunnel junction into an STT-MRAM disk-shaped cell changes substantially the offset field, as the reduction of the lateral dimension comes with the generation of stray fields by the reference and the hard layer. The experimental offset field compares best with the spatial average of the sum of these stray fields, thereby providing guidelines for the offset field engineering.Comment: Special issue of J. Phys. D: Appl. Phys (2019) on STT-MRA

Backward whirl in a simple rotor supported on hydrodynamic bearings

The asymmetric nature of the fluid film stiffness and damping properties in rotors supported on fluid film bearings causes a forward or a backward whirl depending on the bearing parameters and the speed of the rotor. A rotor was designed to exhibit backward synchronous whirl. The rotor-bearing system exhibited split criticals, and a backward whirl was observed between the split criticals. The orbital diagrams show the whirl pattern

Radio halos in merging clusters of galaxies

We present the preliminary results of 235 MHz, 327 MHz and 610 MHz observations of the galaxy cluster A3562 in the core of the Shapley Concentration. The purpose of these observations, carried out with the Giant Metrewave Radio Telescope (GMRT, Pune, India) was to study the radio halo located at the centre of A3562 and determine the shape of its radio spectrum at low frequencies, in order to understand the origin of this source. In the framework of the re--acceleration model, the preliminary analysis of the halo spectrum suggests that we are observing a young source (few $10^8$ yrs) at the beginning of the re--acceleration phase.Comment: 3 pages, 2 figures. Proceedings of IAU Colloquium 195 - Outskirts of Galaxy Clusters: intense life in the suburb

On intersections of ranges of projections of norm one in Banach spaces

In this short note we are interested in studying Banach spaces in which the range of a projection of norm one whose kernel is of finite dimension, is the intersection of ranges of finitely many projections of norm one, whose kernels are of dimension one. We show that for certain class of Banach spaces X, the natural duality between X and X** can be exploited when the range of the projection is of finite codimension. We show that if X* is isometric to L1(µ), then any central subspace of finite codimension, is an intersection of central subspaces of codimension one . These results extend a recent result of Bandyopadhyay and Dutta [2] proved for continuous function spaces and unifies some earlier work of Baronti and Papini, [4], [3]

Nice surjections on spaces of operators

A bounded linear operator is said to be nice if its adjoint preserves extreme points of the dual unit ball. Motivated by a description due to Labuschagne and Mascioni [9] of such maps for the space of compact operators on a Hilbert space, in this article we consider a description of nice surjections on K(X, Y) for Banach spaces X, Y. We give necessary and sufficient conditions when nice surjections are given by composition operators. Our results imply automatic continuity of these maps with respect to other topologies on spaces of operators. We also formulate the corresponding result for L(X, Y) thereby proving an analogue of the result from [9] for Lp(1 < p ≠ 2 < ∞ ) spaces. We also formulate results when nice operators are not of the canonical form, extending and correcting the results from [8]