Let (T,d) be a countable, unbounded and locally finite metric space, and let L_μ ^0(T) be a little weighted Banach space. We study hypercyclic algebras for composition operators on L_μ ^0(T) endowed with a weighted coordinatewise product. We characterize when a single composition operator supports a hypercyclic algebra and give sufficient conditions for the existence of an upper frequently hypercyclic algebra. For a finite family of bounded composition operators C_φ _1,… ,C_φ _N , N≥ 2 , we assume that the symbols are injective and that their iterate sequences are pairwise eventually separated. Under these assumptions, we characterize dense d -hypercyclicity by weight decay conditions along a common sequence of iterates and show that it is equivalent to the existence of a residual set of vectors all of whose positive powers are disjoint hypercyclic. As a consequence, we derive sufficient conditions for such families to support disjoint hypercyclic algebras.
Motivated by the foundational result that a monomial complete intersection has the strong Lefschetz property (SLP) in characteristic zero, it is natural to ask when monomial almost complete intersections have the SLP. In this paper, using the Hilbert series as a central tool, we investigate the strong Lefschetz property for certain monomial almost complete intersections: those with the non-pure-power generator having support in two variables, and those with symmetric Hilbert series. In the former case, we give a complete classification for when the SLP holds, and in the latter case, we prove that such algebras always have the SLP.
In this article, we address a question raised in Dao et al. (Trans Am Math Soc Ser B 10:355–380, 2023) regarding the preservation of reflexivity under taking trace. We answer this question negatively. We also study a few cases where the question has a positive answer in a one dimensional analytically unramified local Cohen-Macaulay ring.
This paper establishes new rigidity theorems for complete spacelike xi-translator immersed in the pseudo-Euclidean space R-p(n+p) . By imposing suitable upper bounds on the norm parallel to xi parallel to or geometric constraints on the norm of the second fundamental form parallel to A parallel to, we apply generalized maximum principles due to Da Silva, Lima Jr. and de Lima (Arch Math 118:663-673, 2022), Chen and Qiu (Adv Math 294:517-531, 2016), and Alias, Caminha and Nascimento (J Math Anal Appl 474: 242-247, 2019). These conditions force the vanishing of the second fundamental form, implying that any such xi-translator is necessarily a spacelike hyperplane of Rn+p (p) .
