Search results for "SPACES"
showing 10 items of 425 documents
On the arithmetically Cohen-Macaulay property for sets of points in multiprojective spaces
2017
We study the arithmetically Cohen-Macaulay (ACM) property for finite sets of points in multiprojective spaces, especially ( P 1 ) n (\mathbb P^1)^n . A combinatorial characterization, the ( ⋆ ) (\star ) -property, is known in P 1 × P 1 \mathbb P^1 \times \mathbb P^1 . We propose a combinatorial property, ( ⋆ s ) (\star _s) with 2 ≤ s ≤ n 2\leq s\leq n , that directly generalizes the ( ⋆ ) (\star ) -property to ( P 1 ) n (\mathbb P^1)^n for larger n n . We show that X X is ACM if and only if it satisfies the ( ⋆ n ) (\star _n) -property. The main tool for several of our results is an extension to the multiprojective setting of certain liaison methods in projective space.
Local spectral theory for Drazin invertible operators
2016
Abstract In this paper we investigate the transmission of some local spectral properties from a bounded linear operator R, as SVEP, Dunford property (C), and property (β), to its Drazin inverse S, when this does exist.
Hardy inequalities and Assouad dimensions
2017
We establish both sufficient and necessary conditions for weighted Hardy inequalities in metric spaces in terms of Assouad (co)dimensions. Our sufficient conditions in the case where the complement is thin are new even in Euclidean spaces, while in the case of a thick complement we give new formulations for previously known sufficient conditions which reveal a natural duality between these two cases. Our necessary conditions are rather straight-forward generalizations from the unweighted case, but together with some examples they indicate the essential sharpness of our results. In addition, we consider the mixed case where the complement may contain both thick and thin parts.
Special arrangements of lines: Codimension 2 ACM varieties in P 1 × P 1 × P 1
2019
In this paper, we investigate special arrangements of lines in multiprojective spaces. In particular, we characterize codimension 2 arithmetically Cohen–Macaulay (ACM) varieties in [Formula: see text], called varieties of lines. We also describe their ACM property from a combinatorial algebra point of view.
Local Spectral Theory for R and S Satisfying RnSRn = Rj
2020
In this paper, we analyze local spectral properties of operators R,S and RS which satisfy the operator equations RnSRn=Rj and SnRSn=Sj for same integers j&ge
Fine properties of functions with bounded variation in Carnot-Carathéodory spaces
2019
Abstract We study properties of functions with bounded variation in Carnot-Caratheodory spaces. We prove their almost everywhere approximate differentiability and we examine their approximate discontinuity set and the decomposition of their distributional derivatives. Under an additional assumption on the space, called property R , we show that almost all approximate discontinuities are of jump type and we study a representation formula for the jump part of the derivative.
Common fixed points for self mappings on compact metric spaces
2013
In this paper we obtain a result of existence of points of coincidence and of common fixed points for two self mappings on compact metric spaces satisfying a contractive condition of Suzuki type. We also present some examples to illustrate our results. Moreover, using the scalarization method of Du, we deduce a result of common fixed point in compact cone metric spaces.
Multiprojective spaces and the arithmetically Cohen-Macaulay property
2019
AbstractIn this paper we study the arithmetically Cohen-Macaulay (ACM) property for sets of points in multiprojective spaces. Most of what is known is for ℙ1× ℙ1and, more recently, in (ℙ1)r. In ℙ1× ℙ1the so called inclusion property characterises the ACM property. We extend the definition in any multiprojective space and we prove that the inclusion property implies the ACM property in ℙm× ℙn. In such an ambient space it is equivalent to the so-called (⋆)-property. Moreover, we start an investigation of the ACM property in ℙ1× ℙn. We give a new construction that highlights how different the behavior of the ACM property is in this setting.
Homomorphisms between Algebras of Holomorphic Functions
2014
For two complex Banach spaces X and Y, in this paper, we study the generalized spectrum M-b(X,Y) of all nonzero algebra homomorphisms from H-b(X), the algebra of all bounded type entire functions on X into H-b(Y). We endow M-b(X,Y) with a structure of Riemann domain over L(X*,Y*) whenever.. is symmetrically regular. The size of the fibers is also studied. Following the philosophy of ( Aron et al., 1991), this is a step to study the set M-b,M-infinity (X,B-Y) of all nonzero algebra homomorphisms from Hb(b) (X) into H-infinity (B-Y) of bounded holomorphic functions on the open unit ball of Y and M-infinity(B-X,B-Y) of all nonzero algebra homomorphisms from H-infinity(B-X) into H infinity (B-Y…
Bing meets Sobolev
2019
We show that, for each $1\le p < 2$, there exists a wild involution $\mathbb S^3\to \mathbb S^3$ in the Sobolev class $W^{1,p}(\mathbb S^3,\mathbb S^3)$.