https://www.mscand.dk/issue/feed MATHEMATICA SCANDINAVICA 2020-06-06T03:29:26+02:00 Andrew Swann mscand@math.au.dk Open Journal Systems https://www.mscand.dk/article/view/116324 Remarks on vector space generated by the multiplicative commutators of a division ring 2020-06-06T03:29:15+02:00 M. Aaghabali mscand@math.au.dk Z. Tajfirouz mscand@math.au.dk <p>Let $D$ be a division ring with centre $F$. An element of the form $xyx^{-1}y^{-1}\in D$ is called a multiplicative commutator. Let $T(D)$ be the vector space over $F$ generated by all multiplicative commutators in $D$. In M.&nbsp;Aghabali et al., J. Algebra Appl. 12 (2013), no.&nbsp;8, art.&nbsp;1350043, the authors have conjectured that every division ring is generated as a vector space over its centre by all of its multiplicative commutators. In this note it is shown that if $D$ is centrally finite, then the conjecture holds.</p> 2020-05-06T00:00:00+02:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/119227 An upper bound for the regularity of powers of edge ideals 2020-06-06T03:28:49+02:00 Jürgen Herzog mscand@math.au.dk Takayuki Hibi mscand@math.au.dk <p>For a finite simple graph $G$ we give an upper bound for the regularity of the powers of the edge ideal $I(G)$.</p> 2020-05-06T00:00:00+02:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/119672 On Ratliff-Rush closure of modules 2020-06-06T03:28:18+02:00 Naoki Endo mscand@math.au.dk <p>In this paper, we introduce the notion of Ratliff-Rush closure of modules and explore whether the condition of the Ratliff-Rush closure coincides with the integral closure. The main result characterizes the condition in terms of the normality of the projective scheme of the Rees algebra. In conclusion, we shall give a criterion for the Buchsbaum Rees algebras.</p> 2020-05-06T00:00:00+02:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/119382 Cohen-Macaulay homological dimensions 2020-06-06T03:28:33+02:00 Parviz Sahandi mscand@math.au.dk Tirdad Sharif mscand@math.au.dk Siamak Yassemi mscand@math.au.dk <p>We introduce new homological dimensions, namely the Cohen-Macaulay projective, injective and flat dimensions for homologically bounded complexes. Among other things we show that (a)&nbsp;these invariants characterize the Cohen-Macaulay property for local rings, (b)&nbsp;Cohen-Macaulay flat dimension fits between the Gorenstein flat dimension and the large restricted flat dimension, and (c)&nbsp;Cohen-Macaulay injective dimension fits between the Gorenstein injective dimension and the Chouinard invariant.</p> 2020-05-06T00:00:00+02:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/119740 Little dimension and the improved new intersection theorem 2020-06-06T03:28:03+02:00 Tsutomu Nakamura mscand@math.au.dk Ryo Takahashi mscand@math.au.dk Siamak Yassemi mscand@math.au.dk <p>Let $R$ be a commutative noetherian local ring. We define a new invariant for $R$-modules which we call the little dimension. Using it, we extend the improved new intersection theorem.</p> 2020-05-06T00:00:00+02:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/119216 A smoothness criterion for complex spaces in terms of differential forms 2020-06-06T03:28:54+02:00 Håkan Samuelsson Kalm mscand@math.au.dk Martin Sera mscand@math.au.dk <p>For a reduced pure dimensional complex space $X$, we show that if Barlet's recently introduced sheaf $\alpha _X^1$ of holomorphic $1$-forms or the sheaf of germs of weakly holomorphic $1$-forms is locally free, then $X$ is smooth. Moreover, we discuss the connection to Barlet's well-known sheaf $\omega _X^1$.</p> 2020-05-06T00:00:00+02:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/119234 Hausdorff dimension of limsup sets of rectangles in the Heisenberg group 2020-06-06T03:28:44+02:00 Fredrik Ekström mscand@math.au.dk Esa Järvenpää mscand@math.au.dk Maarit Järvenpää mscand@math.au.dk <p>The almost sure value of the Hausdorff dimension of limsup sets generated by randomly distributed rectangles in the Heisenberg group is computed in terms of directed singular value functions.</p> 2020-05-06T00:00:00+02:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/115974 Extension of positive maps 2020-06-06T03:29:26+02:00 Erling Størmer mscand@math.au.dk <p>We prove an extension theorem for positive maps from operator systems into matrix algebras</p> 2020-05-06T00:00:00+02:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/116244 Local boundedness for minimizers of convex integral functionals in metric measure spaces 2020-06-06T03:29:21+02:00 Huiju Wang mscand@math.au.dk Pengcheng Niu mscand@math.au.dk <p>In this paper we consider the convex integral functional $I := \int _\Omega {\Phi (g_u)\,d\mu }$ in the metric measure space $(X,d,\mu )$, where $X$ is a set, $d$ is a metric, µ is a Borel regular measure satisfying the doubling condition, Ω is a bounded open subset of $X$, $u$ belongs to the Orlicz-Sobolev space $N^{1,\Phi }(\Omega )$, Φ is an N-function satisfying the $\Delta _2$-condition, $g_u$ is the minimal Φ-weak upper gradient of $u$. By improving the corresponding method in the Euclidean space to the metric setting, we establish the local boundedness for minimizers of the convex integral functional under the assumption that $(X,d,\mu )$ satisfies the $(1,1)$-Poincaré inequality. The result of this paper can be applied to the Carnot-Carathéodory space spanned by vector fields satisfying Hörmander's condition.</p> 2020-05-06T00:00:00+02:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/119079 Compact group actions on operator algebras and their spectra 2020-06-06T03:29:04+02:00 Costel Peligrad mscand@math.au.dk <p>We consider a class of dynamical systems with compact non-abelian groups that include C*-, W*- and multiplier dynamical systems. We prove results that relate the algebraic properties such as simplicity or primeness of the fixed point algebras to the spectral properties of the action, including the Connes and strong Connes spectra.</p> 2020-05-06T00:00:00+02:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/119209 An interpolation of Ohno's relation to complex functions 2020-06-06T03:28:59+02:00 Minoru Hirose mscand@math.au.dk Hideki Murahara mscand@math.au.dk Tomokazu Onozuka mscand@math.au.dk <p>Ohno's relation is a well known formula among multiple zeta values. In this paper, we present its interpolation to complex functions.</p> 2020-05-06T00:00:00+02:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/117570 Periodic codings of Bratteli-Vershik systems 2020-06-06T03:29:10+02:00 Sarah Frick mscand@math.au.dk Karl Petersen mscand@math.au.dk Sandi Shields mscand@math.au.dk <p>We develop conditions for the coding of a Bratteli-Vershik system according to initial path segments to be periodic, equivalently for a constructive symbolic recursive scheme corresponding to a cutting and stacking process to produce a periodic sequence. This is a step toward understanding when a Bratteli-Vershik system can be essentially faithfully represented by means of a natural coding as a subshift on a finite alphabet.</p> 2020-05-06T00:00:00+02:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/119260 Spectral triples for higher-rank graph $C^*$-algebras 2020-06-06T03:28:39+02:00 Carla Farsi mscand@math.au.dk Elizabeth Gillaspy mscand@math.au.dk Antoine Julien mscand@math.au.dk Sooran Kang mscand@math.au.dk Judith Packer mscand@math.au.dk <p>In this note, we present a new way to associate a spectral triple to the noncommutative $C^*$-algebra $C^*(\Lambda )$ of a strongly connected finite higher-rank graph Λ. Our spectral triple builds on an approach used by Consani and Marcolli to construct spectral triples for Cuntz-Krieger algebras. We prove that our spectral triples are intimately connected to the wavelet decomposition of the infinite path space of Λ which was introduced by Farsi, Gillaspy, Kang, and Packer in 2015. In particular, we prove that the wavelet decomposition of Farsi et al.&nbsp;describes the eigenspaces of the Dirac operator of our spectral triple. The paper concludes by discussing other properties of the spectral triple, namely, θ-summability and Brownian motion.</p> 2020-05-06T00:00:00+02:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/119601 On the convergence of iterates of convolution operators in Banach spaces 2020-06-06T03:28:26+02:00 Heybetkulu Mustafayev mscand@math.au.dk <p>Let $G$ be a locally compact abelian group and let $M(G)$ be the measure algebra of $G$. A measure $\mu \in M(G)$ is said to be power bounded if $\sup _{n\geq 0}\lVert \mu ^{n} \rVert _{1}&lt;\infty$. Let $\mathbf {T} = \{ T_{g}:g\in G\}$ be a bounded and continuous representation of $G$ on a Banach space $X$. For any $\mu \in M(G)$, there is a bounded linear operator on $X$ associated with µ, denoted by $\mathbf {T}_{\mu }$, which integrates $T_{g}$ with respect to µ. In this paper, we study norm and almost everywhere behavior of the sequences $\{ \mathbf {T}_{\mu }^{n}x\}$ $(x\in X)$ in the case when µ is power bounded. Some related problems are also discussed.</p> 2020-05-06T00:00:00+02:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/119684 Generalized adjoints and applications to composition operators 2020-06-06T03:28:13+02:00 Geraldo Botelho mscand@math.au.dk Leodan A. Torres mscand@math.au.dk <p>We generalize the classical notion of adjoint of a linear operator and the Aron-Schottenloher notion of adjoint of a homogeneous polynomial. The general (nonlinear) notion is shown to enjoy several properties enjoyed by the classical (linear) ones, nevertheless new interesting phenomena arise in the nonlinear theory. The proofs are not always simple adaptations of the linear cases, actually nonlinear arguments are often required. Applications of the generalized adjoints to Lindström-Schlüchtermann type theorems for composition operators are provided.</p> 2020-05-06T00:00:00+02:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/119699 Some remarks on $\mathrm{K}_0$ of noncommutative tori 2020-06-06T03:28:08+02:00 Sayan Chakraborty mscand@math.au.dk <p>Using Rieffel's construction of projective modules over higher dimensional noncommutative tori, we construct projective modules over some continuous field of C*-algebras whose fibres are noncommutative tori. Using a result of Echterhoff et al., our construction gives generators of $\mathrm {K}_0$ for all noncommutative tori.</p> 2020-05-06T00:00:00+02:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/120072 Issue covers 2020-05-06T09:51:36+02:00 Mathematica Scandinavica mscand@math.au.dk <p>Issue covers</p> 2020-05-06T00:00:00+02:00 ##submission.copyrightStatement##