@article {7474,
	title = {Generalized Krein algebras and asymptotics of Toeplitz determinants},
	journal = {Methods of Functional Analysis and Topology},
	volume = {13},
	year = {2007},
	pages = {236-261},
	abstract = {<script src={\textquoteright}https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML{\textquoteright}></script><p>We give a survey on generalized Krein algebras \(K_{p,q}^{\alpha,\beta}\) and their applications to Toeplitz determinants. Our methods originated in a paper by Mark Krein of 1966, where he showed that \(K_{2,2}^{1/2,1/2}\) is a Banach algebra. Subsequently, Widom proved the strong Szeg\H{o} limit theorem for block Toeplitz determinants with symbols in \((K_{2,2}^{1/2,1/2})_{N\times N}\) and later two of the authors studied symbols in the generalized Krein algebras \((K_{p,q}^{\alpha,\beta})_{N\times N}\), where \(\lambda:=1/p+1/q=\alpha+\beta\) and \(\lambda=1\). We here extend these results to \(0\&lt;\lambda\&lt;1\). The entire paper is based on fundamental work by Mark Krein, ranging from operator ideals through Toeplitz operators up to Wiener-Hopf factorization.</p>
},
	url = {http://mfat.imath.kiev.ua/},
	author = {B{\"o}ttcher, Albrecht and Karlovich, Alexei Yu. and Bernd Silbermann}
}
