Property (ω) and quasi-class (A, k) operators
In this paper, we prove the following assertions: (i) If T is of quasi-class (A, k), then T is polaroid and reguloid; (ii) If T or T* is an algebraically of quasi-class (A, k) operator, then Weyls theorem holds for f(T) for every f ∈ Hol(σ(T)); (iii) If T* is an algebraically of quasi-class (A, k) operator, then a-Weyls theorem holds for f(T) for every f ∈ Hol(σ(T)); (iv) If T* is algebraically of quasi-class (A, k) then property (ω) holds for T.
Properties (t) and (gt) for Bounded Linear Operators
In this paper we introduce and study the properties (t) and (gt), which extend properties (w) and (gw). We establish for a bounded linear operator defined on a Banach space several sufficient and necessary conditions for which property (t) and property (gt) hold. We also relate these properties with Weyl’s type theorems. We show that if T is a bounded linear operator acting on a Banach space X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\fancyscript{X}}$$\end{document}, then property (gt) holds for T if and only if property (gw) holds for T and σ(T) = σa(T). Analogously, we show that property (t) holds for T if and only if property (ω) holds for T and σ(T) = σa(T). We also study the properties (t) and (gt) for the operators satisfying the single valued extension property. Moreover, these properties are also studied in the framework of polaroid operators.
Frequency distributions of the mixing height over an urban area from SODAR data
The height of the mixing-layer (MLH) is an important parameter in the assessment of the dilution of primarily emitted or secondarily formed air pollutants in the atmospheric boundary-layer. A continuous measurement of MLH is possible only by remote sensing. Here, 17 months of SODAR data have been analysed automatically to derive the MLH over the city of Hannover in Northern Germany. In contrast to earlier studies the MLH has been determined from vertical profiles of the acoustic backscatter intensity and from the variance of the vertical velocity component. The results are presented in form of monthly frequency distributions and mean daily courses of MLH. These statistical evaluations of MLH show a clear annual course and interannual variability. The study shows the possibility to derive meaningful climatological information from long-term SODAR measurements for air quality issues.