ACTA SCIENTIARUM MATHEMATICARUM最新文献

A convex geometry is a closure system satisfying the anti-exchange property. This paper, following the work of Adaricheva and Bolat (Discrete Math 342(N3):726–746, 2019) and the Polymath REU 2020 team (Convex geometries representable by at most 5 circles on the plane. arXiv:2008.13077), continues to investigate representations of convex geometries on a 5-element base set. It introduces several properties: the opposite property, nested triangle property, area Q property, and separation property, of convex geometries of circles on a plane, preventing this representation for numerous convex geometries on a 5-element base set. It also demonstrates that all 672 convex geometries on a 5-element base set have a representation by ellipses, as given in the appendix for those without a known representation by circles, and introduces a method of expanding representation with circles by defining unary predicates, shown as colors.

In this paper, we investigate Banach lattices on which each positive semi-compact operator (T: Erightarrow F) is null almost L-weakly compact (rep. Null almost M-weakly compact). Additionally, we present certain sufficient and necessary conditions for a positive Null almost L-weakly compact operator to be semi-compact.

In this paper, we obtain some upper bounds for the singular values of sums of product of matrices. The obtained forms involve direct sums and mean-like matrix quantities. As applications, several bounds will be found in terms of the Aluthge transform, matrix means, matrix monotone functions and accretive-dissipative matrices. For example, we show that if X is an (ntimes n) accretive-dissipative matrix, then

for (j=1,2,ldots n), where (s_j(cdot ), Re (cdot )) and (Im (cdot )) denote the (j-)th singular value, the real part and the imaginary part, respectively. We also show that if (sigma _f,sigma _g) are two matrix means corresponding to the operator monotone functions f, g, then

for (j =1,2, ldots , n), where A, B are two positive definite (ntimes n) matrices.

The main purpose of this paper is to investigate the relationship between continuation of pluriharmonic functions from the boundary of an unbounded domain and the vanishing of the Bott-Chern cohomology with supports in a paracompactifying family of closed subset of a complex manifold X. We moreover give a relation between distributional boundary values and extensible currents.

We give several basic and spectral properties of classes of closed n-paranormal and closed (n^{*})-paranormal operators on dense domains in complex separable Hilbert spaces. We prove that for both of these classes of operators, the null space of ((T-mu I)) and the range of (R(E_{mu })) are identical, where (E_{mu }) is the Riesz projection with respect to an isolated point (mu ) of the spectrum. We show that they satisfy Weyl’s theorem. Certain properties related to the reduced minimum modulus are also established.

In this paper, we establish the stability of uaw-convergence under passing from sublattices. The various implications of this fact are presented through the paper. In particular, we show that if ((x_{alpha })) is an increasing net in a Banach lattice E and (x_{alpha }overset{uaw}{longrightarrow }0) in E then (x_{alpha }overset{un}{longrightarrow }0) in (E^{''}). Furthermore, we deduce some results concerning uaw-completeness. Additionally, we present a new characterizations of KB-spaces (resp. reflexive Banach lattices), using the concepts of uaw-convergence and un-convergence.

In this article, we study strongly convex matrix functions and the strong Davis-Sherman condition to see their relations, corresponding to those of strongly operator-convex functions in Brown (Can J Math 40:865–988, 1988; Ann Funct Anal 9:41–55, 2018)and in Brown and Uchiyama(Linear Algebra Appl) Linear Algebra Appl 553:238–251, 2018).