Group inversion in certain finite-dimensional algebras generated by two idempotents

Invertibility in Banach algebras generated by two idempotents can be checked with the help of a theorem by Roch, Silbermann, Gohberg, and Krupnik. This theorem cannot be used to study generalized invertibility. The present paper is devoted to group invertibility in two types of finite-dimensional algebras which are generated by two idempotents, algebras generated by two tightly coupled idempotents on the one hand and algebras of dimension at most four on the other. As a side product, the paper gives the classification of all at most four-dimensional algebras which are generated by two idempotents. (c) 2012 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved

Drazin inversion in the von Neumann algebra generated by two orthogonal projections

Criteria for Drazin and Moore-Penrose invertibility of operators in the von Neumann algebra generated by two orthogonal projections are established and explicit representations for the corresponding inverses are given. The results are illustrated by several examples that have recently been considered in the literature. (C) 2009 Elsevier Inc. All rights reserved

A gentle guide to the basics of two projections theory

This paper is a survey of the basics of the theory of two projections. It contains in particular the theorem by Halmos on two orthogonal projections and Roch, Silbermann, Gohberg, and Krupnik\u27s theorem on two idempotents in Banach algebras. These two theorems, which deliver the desired results usually very quickly and comfortably, are missing or wrongly cited in many recent publications on the topic, The paper is intended as a gentle guide to the field. The basic theorems are precisely stated, some of them are accompanied by full proofs, others not, but precise references are given in each case, and many examples illustrate how to work with the theorems. (C) 2009 Elsevier Inc. All rights reserved

Toeplitz operators of finite interval type and the table method

We solve a Riemann-Hilbert problem with almost periodic coefficient G, associated to a Toeplitz operator T-G in a class which is closely connected to finite interval convolution equations, based on a generalization of the so-called table method. The explicit determination of solutions to that problem allows one to establish necessary and sufficient conditions for the invertibility of the corresponding Toeplitz operator, and to determine an appropriate factorization of G, providing explicit formulas for the inverse of T-G. Some unexpected properties of the Fourier spectrum of the solutions are revealed which are not apparent through other approaches to the same probleminfo:eu-repo/semantics/acceptedVersio

Revised Pulsar Spindown

We address the issue of electromagnetic pulsar spindown by combining our experience from the two limiting idealized cases which have been studied in great extent in the past: that of an aligned rotator where ideal MHD conditions apply, and that of a misaligned rotator in vacuum. We construct a spindown formula that takes into account the misalignment of the magnetic and rotation axes, and the magnetospheric particle acceleration gaps. We show that near the death line aligned rotators spin down much slower than orthogonal ones. In order to test this approach, we use a simple Monte Carlo method to simulate the evolution of pulsars and find a good fit to the observed pulsar distribution in the P-Pdot diagram without invoking magnetic field decay. Our model may also account for individual pulsars spinning down with braking index n < 3, by allowing the corotating part of the magnetosphere to end inside the light cylinder. We discuss the role of magnetic reconnection in determining the pulsar braking index. We show, however, that n ~ 3 remains a good approximation for the pulsar population as a whole. Moreover, we predict that pulsars near the death line have braking index values n > 3, and that the older pulsar population has preferentially smaller magnetic inclination angles. We discuss possible signatures of such alignment in the existing pulsar data.Comment: 8 pages, 7 figures; accepted to Ap

Weibel instability and associated strong fields in a fully 3D simulation of a relativistic shock

Plasma instabilities (e.g., Buneman, Weibel and other two-stream instabilities) excited in collisionless shocks are responsible for particle (electron, positron, and ion) acceleration. Using a new 3-D relativistic particle-in-cell code, we have investigated the particle acceleration and shock structure associated with an unmagnetized relativistic electron-positron jet propagating into an unmagnetized electron-positron plasma. The simulation has been performed using a long simulation system in order to study the nonlinear stages of the Weibel instability, the particle acceleration mechanism, and the shock structure. Cold jet electrons are thermalized and slowed while the ambient electrons are swept up to create a partially developed hydrodynamic (HD) like shock structure. In the leading shock, electron density increases by a factor of 3.5 in the simulation frame. Strong electromagnetic fields are generated in the trailing shock and provide an emission site. We discuss the possible implication of our simulation results within the AGN and GRB context.Comment: 4 pages, 3 figures, ApJ Letters, in pres

The Double Pulsar Eclipses I: Phenomenology and Multi-frequency Analysis

The double pulsar PSR J0737-3039A/B displays short, 30 s eclipses that arise around conjunction when the radio waves emitted by pulsar A are absorbed as they propagate through the magnetosphere of its companion pulsar B. These eclipses offer a unique opportunity to probe directly the magnetospheric structure and the plasma properties of pulsar B. We have performed a comprehensive analysis of the eclipse phenomenology using multi-frequency radio observations obtained with the Green Bank Telescope. We have characterized the periodic flux modulations previously discovered at 820 MHz by McLaughlin et al., and investigated the radio frequency dependence of the duration and depth of the eclipses. Based on their weak radio frequency evolution, we conclude that the plasma in pulsar B's magnetosphere requires a large multiplicity factor (~ 10^5). We also found that, as expected, flux modulations are present at all radio frequencies in which eclipses can be detected. Their complex behavior is consistent with the confinement of the absorbing plasma in the dipolar magnetic field of pulsar B as suggested by Lyutikov & Thompson and such a geometric connection explains that the observed periodicity is harmonically related to pulsar B's spin frequency. We observe that the eclipses require a sharp transition region beyond which the plasma density drops off abruptly. Such a region defines a plasmasphere which would be well inside the magnetospheric boundary of an undisturbed pulsar. It is also two times smaller than the expected standoff radius calculated using the balance of the wind pressure from pulsar A and the nominally estimated magnetic pressure of pulsar B.Comment: 9 pages, 7 figures, 3 tables, ApJ in pres