arXiv subjects
Publications and source records attributed to D. V. Zanin.
We present a systematic study of asymptotic behavior of (generalised) $ζ-$functions and heat kernels used in noncommutative geometry and clarify their connections with Dixmier traces. We strengthen and complete a number of results from the recent literature and answer (in the affirmative) the question raised by M. Benameur and T. Fack \cite{BF}.
The Kruglov property and the Kruglov operator play an important role in the study of geometric properties of r.i. function spaces. We prove that the boundedness of the Kruglov operator in a r.i. space is equivalent to the uniform boundedness on this space of a sequence of operators defined by random permutations. It is shown also that there is no minimal r.i. space with the Kruglov property.
We establish several analogues of the classical Lidskii Theorem for some special classes of singular traces (Dixmier traces and Connes-Dixmier traces) used in noncommutative geometry.
Suppose $E$ is fully symmetric Banach function space on $(0,1)$ or $(0,\infty)$ or a fully symmetric Banach sequence space. We give necessary and sufficient conditions on $f\in E$ so that its orbit $Ω(f)$ is the closed convex hull of its extreme points. We also give an application to symmetrically normed ideals of compact operators on a Hilbert space.
In this paper we consider quadratic stochastic operators designed on finite Abelian groups. It is proved that such operators have the property of regularity.