Characterizations of symmetrized polydisc

Abstract

Let Γ n , n ≥ 2, denote the symmetrized polydisc in C n , and Γ 1 be the closed unit disc in C. We provide some characterizations of elements in Γ n . In particular, an element (s 1 , . . . , s n−1 , p) ∈ C n is in Γ n if and only if s

Normal Paradistributive Latticoids

“…He established that a distributive lattice A with 0 is normal iff for all x, y ∈ A, x ∧ y = 0 implies x ⊥ and y ⊥ are comaximal. Pawar [4] characterized normal lattices using the properties of Stone space of prime filters and the Stone space of maximal filters of a bounded distributive lattice. In 1977, Pawar and Thakare [5] introduced pm-lattices as bounded distributive lattices where each prime ideal is uniquely contained within a maximal ideal.…”

Algebraic Properties of Toeplitz operators on the symmetrized polydisk

“…The goal of this paper is to extend the theory of Toeplitz operators in the Hardy space setting to another domain in C d , d ≥ 2, viz., the symmetrized polydisk. This polynomially convex but not convex domain has attracted a considerable amount of attention for its complex geometry [19,17,24,25,23], function theory [22,26,31], and operator theory [10]. To describe the domain, we consider the elementary symmetric functions s i : C d → C of degree i in d variables defined as s 0 := 1 and s i (z) :=…”