Denseness for norm attaining operator-valued functions
Abstract In this note we offer a short, constructive proof for Hilbert spaces of Lindenstrauss' famous result on the denseness of norm attaining operators. Specifically, we show given any A∈ L ( H ) there is a sequence of rank-1 operators K n such that A+K n is norm attaining for each n and K n converges in norm to zero. We then apply our construction to establish denseness results for norm attaining operator-valued functions.
Harnack's theorem for harmonic compact operator-valued functions
Abstract In this paper we show that harmonic compact operator-valued functions are characterized by having harmonic diagonal matrix coefficients in any choice of basis. We also give an example which shows that an operator-valued function with values outside the compact operators can have harmonic diagonal matrix coefficients in any choice of basis without being a harmonic operator-valued function. We use our harmonic matrix coefficients characterization to establish a Harnack's theorem for an increasing sequence of harmonic compact self-adjoint operator-valued functions and we show that this Harnack's theorem need not hold when the compactness restriction is dropped.
Study on quantitative earthquake damage of Dujiangyan city, caused by 2008 MS=8.0 Wenchuan, China earthquake based on aerial imagery
The paper introduces quantitative earthquake damage estimation method based on remote sensing data. The quantitative remote sensing seismic damage index based on building damage extracted from the aerial image of Dujiangyan city proper, southwest China's Sichuan province, which acquired after 2008 Ms=8.0 Wenchuan earthquake. The actual seismic damage indices were determined by the ground-based investigation in the city proper. Then their quantitative relationship was established. The results indicate that it is possible to build quantitative model of remote sensing seismic damage, which will enhance significantly the practicality applying the remote sensing in emergency acquisition and analysis of seismic disaster.