» Dynamics of complex harmonic mappings
20/12/24 10:00 from math.CV updates on arXiv.org
arXiv:2412.14924v1 Announce Type: new Abstract: This note initiates the study of the Fatou\,--\,Julia sets of a complex harmonic mapping. Along with some fundamental properties of the Fatou and the Julia sets, we observe some contrasting...

» On conjugate system with respect to completely positive maps
20/12/24 10:00 from math.OA updates on arXiv.org
arXiv:2412.14336v1 Announce Type: new Abstract: We study the operator-valued partial derivative associated with covariance matrices on a von Neumann algebra B. We provide a cumulant characterization for the existence of conjugate variabl...

» Verlinde rings and cluster algebras arising from quantum affine algebras
20/12/24 10:00 from math.RT updates on arXiv.org
arXiv:2412.14601v1 Announce Type: new Abstract: We formulate a positivity conjecture relating the Verlinde ring associated with an untwisted affine Lie algebra at a positive integer level and a subcategory of finite-dimensional represent...

» A nontrivial uniform algebra Dirichlet on its maximal ideal space
20/12/24 10:00 from math.CV updates on arXiv.org
arXiv:2403.19583v3 Announce Type: replace Abstract: It is shown that there exists a nontrivial uniform algebra that is Dirichlet on its maximal ideal space and has a dense set of elements that are exponentials. This answers a 64-year-old...

» Characterization of minimal tripotents via annihilators and its application to the study of additive preservers of truncations
20/12/24 10:00 from math.OA updates on arXiv.org
arXiv:2412.14394v1 Announce Type: new Abstract: The contributions in this note begin with a new characterization of (positive) scalar multiples of minimal tripotents in a general JB$^*$-triple $E$, proving that a non-zero element $a\in E...

» Construction of Toda flow via Sato-Segal-Wilson theory
20/12/24 10:00 from math.SP updates on arXiv.org
arXiv:2412.14463v1 Announce Type: new Abstract: A Toda flow is constructed on a space of bounded initial data through Sato-Segal-Wilson theory. The flow is described by the Weyl functions of the underlying Jacobi operators. This is a con...

» $\ell^1$-bases, algebraic structure and strong Arens irregularity of Banach algebras in harmonic analysis$^1$
20/12/24 10:00 from math.OA updates on arXiv.org
arXiv:2412.15029v1 Announce Type: cross Abstract: A long standing problem in abstract harmonic analysis concerns the strong Arens irregularity (sAir, for short) of the Fourier algebra $A(G)$ of a locally compact group $G.$ The groups for...

» Homology of Steinberg algebras
20/12/24 10:00 from math.OA updates on arXiv.org
arXiv:2412.15112v1 Announce Type: cross Abstract: We study homological invariants of the Steinberg algebra $\mathcal{A}_k(\mathcal{G})$ of an ample groupoid $\mathcal{G}$ over a commutative ring $k$. For $\mathcal{G}$ principal or Hausdo...