Diagonal Multilinear Operators on K\"othe Sequence Spaces

We analyze the interplay between maximal/minimal/adjoint ideals of multilinear operators (between sequence spaces) and their associated K\"othe sequence spaces. We establish relationships with spaces of multipliers and apply these results to describe diagonal multilinear operators from Lorentz sequence spaces. We also define and study some properties of the ideal of $(E;p)$-summing multilinear mappings, a natural extension of the linear ideal of absolutely $(E;p)$-summing operators

Bilinear Ideals in Operator Spaces

We introduce a concept of bilinear ideal of jointly completely bounded mappings between operator spaces. In particular, we study the bilinear ideals $\mathcal{N}$ of completely nuclear, $\mathcal{I }$ of completely integral, $\mathcal{E}$ of completely extendible bilinear mappings, $\mathcal{MB}$ multiplicatively bounded and its symmetrization $\mathcal{SMB}$. We prove some basic properties of them, one of which is the fact that $\mathcal{I}$ is naturally identified with the ideal of (linear) completely integral mappings on the injective operator space tensor product.Comment: 24 pages, accepted for publication in Journal of Mathematical Analysis and Application

Simulations of secondary Farley-Buneman instability driven by a kilometer-scale primary wave: anomalous transport and formation of flat-topped electric fields

Since the 1950s, high frequency and very high frequency radars near the magnetic equator have frequently detected strong echoes caused ultimately by the Farley‐Buneman instability (FBI) and the gradient drift instability (GDI). In the 1980s, coordinated rocket and radar campaigns made the astonishing observation of flat‐topped electric fields coincident with both meter‐scale irregularities and the passage of kilometer‐scale waves. The GDI in the daytime E region produces kilometer‐scale primary waves with polarization electric fields large enough to drive meter‐scale secondary FBI waves. The meter‐scale waves propagate nearly vertically along the large‐scale troughs and crests and act as VHF tracers for the large‐scale dynamics. This work presents a set of hybrid numerical simulations of secondary FBIs, driven by a primary kilometer‐scale GDI‐like wave. Meter‐scale density irregularities develop in the crest and trough of the kilometer‐scale wave, where the total electric field exceeds the FBI threshold, and propagate at an angle near the direction of total Hall drift determined by the combined electric fields. The meter‐scale irregularities transport plasma across the magnetic field, producing flat‐topped electric fields similar to those observed in rocket data and reducing the large‐scale wave electric field to just above the FBI threshold value. The self‐consistent reduction in driving electric field helps explain why echoes from the FBI propagate near the plasma acoustic speed.NSF grants PHY-1500439 and AGS-1755350 and NASA grant NNX14AI13G supported the research presented in this work. This work used TACC and XSEDE computational resources supported by the National Science Foundation grant ACI-1053575. This paper did not use any data; simulation runs are archived on the TACC Ranch system. The authors thank one anonymous reviewer for helpful comments. (PHY-1500439 - NSF; AGS-1755350 - NSF; NNX14AI13G - NASA; ACI-1053575 - National Science Foundation)Published version2019-07-0

Holomorphic Functions and polynomial ideals on Banach spaces

Given \u a multiplicative sequence of polynomial ideals, we consider the associated algebra of holomorphic functions of bounded type, H_{b\u}(E). We prove that, under very natural conditions verified by many usual classes of polynomials, the spectrum M_{b\u}(E) of this algebra "behaves" like the classical case of $M_{b}(E)$ (the spectrum of $H_b(E)$, the algebra of bounded type holomorphic functions). More precisely, we prove that M_{b\u}(E) can be endowed with a structure of Riemann domain over $E"$ and that the extension of each f\in H_{b\u}(E) to the spectrum is an \u-holomorphic function of bounded type in each connected component. We also prove a Banach-Stone type theorem for these algebras.Comment: 19 page

Formation of plasma around a small meteoroid: 2. Implications for radar head echo

This paper calculates the spatial distribution of the plasma responsible for radar head echoes by applying the kinetic theory developed in the companion paper. This results in a set of analytic expressions for the plasma density as a function of distance from the meteoroid. It shows that at distances less than a collisional mean free path from the meteoroid surface, the plasma density drops in proportion to 1/R where R is the distance from the meteoroid center; and, at distances much longer than the mean‐free‐path behind the meteoroid, the density diminishes at a rate proportional to 1/R2. The results of this paper should be used for modeling and analysis of radar head echoes.This work was supported by NSF grant AGS-1244842. (AGS-1244842 - NSF

Generation of electric fields and currents by neutral flows in weakly ionized plasmas through collisional dynamos

In weakly ionized plasmas neutral flows drag plasma across magnetic field lines generating intense electric fields and currents. An example occurs in the Earth's ionosphere near the geomagnetic equator. Similar processes take place in the Solar chromosphere and magnetohydrodynamic generators. This paper argues that not all convective neutral flows generate electric fields and currents and it introduces the corresponding universal criterion for their formation, ∇×(U×B)≠∂B/∂t, where U is the neutral flow velocity, B is the magnetic field, and t is time. This criterion does not depend on the conductivity tensor, σˆ. For many systems, the displacement current, ∂B/∂t, is negligible making the criterion even simpler. This theory also shows that the neutral-dynamo driver that generates E-fields and currents plays the same role as the DC electric current plays for the generation of the magnetic field in the Biot-Savart law.This work was supported by NSF/DOE Grant No. PHY-1500439, NASA Grant Nos. NNX11A096G and NNX14AI13G, and NSF-AGS Postdoctoral Research Fellowship Award No. 1433536. (PHY-1500439 - NSF/DOE; NNX11A096G - NASA; NNX14AI13G - NASA; 1433536 - NSF-AGS

Magnetosphere-Ionosphere Coupling Through E-region Turbulence: Anomalous Conductivities and Frictional Heating

Global magnetospheric MHD codes using ionospheric conductances based on laminar models systematically overestimate the cross-polar cap potential during storm time by up to a factor of two. At these times, strong DC electric fields penetrate to the E region and drive plasma instabilities that create turbulence. This plasma density turbulence induces non-linear currents, while associated electrostatic field fluctuations result in strong anomalous electron heating. These two effects will increase the global ionospheric conductance. Based on the theory of non-linear currents developed in the companion paper, this paper derives the correction factors describing turbulent conductivities and calculates turbulent frictional heating rates. Estimates show that during strong geomagnetic storms the inclusion of anomalous conductivity can double the total Pedersen conductance. This may help explain the overestimation of the cross-polar cap potentials by existing MHD codes. The turbulent conductivities and frictional heating presented in this paper should be included in global magnetospheric codes developed for predictive modeling of space weather.Comment: 13 pages, 5 figures, 2nd of two companion paper

An integral formula for multiple summing norms of operators

We prove that the multiple summing norm of multilinear operators defined on some $n$-dimensional real or complex vector spaces with the $p$-norm may be written as an integral with respect to stables measures. As an application we show inclusion and coincidence results for multiple summing mappings. We also present some contraction properties and compute or estimate the limit orders of this class of operators.Comment: 19 page