共查询到20条相似文献,搜索用时 31 毫秒
1.
The classic Rosenthal–Lacey theorem asserts that the Banach space of continuous real-valued maps on an infinite compact space K has a quotient isomorphic to c or . More recently, Ka?kol and Saxon [20] proved that the space endowed with the pointwise topology has an infinite-dimensional separable quotient algebra iff K has an infinite countable closed subset. Hence lacks infinite-dimensional separable quotient algebras. This motivates the following question: (?) Doesadmit an infinite-dimensional separable quotient (shortly SQ) for any infinite compact space K? Particularly, does admit SQ? Our main theorem implies that has SQ for any compact space K containing a copy of . Consequently, this result reduces problem (?) to the case when K is an Efimov space (i.e. K is an infinite compact space that contains neither a non-trivial convergent sequence nor a copy of ). Although, it is unknown if Efimov spaces exist in ZFC, we show, making use of some result of R. de la Vega (2008) (under ?), that for some Efimov space K the space has SQ. Some applications of the main result are provided. 相似文献
2.
Jan O. Kleppe 《Journal of Pure and Applied Algebra》2018,222(3):610-635
Let be the scheme parameterizing graded quotients of with Hilbert function H (it is a subscheme of the Hilbert scheme of if we restrict to quotients of positive dimension, see definition below). A graded quotient of codimension c is called standard determinantal if the ideal I can be generated by the minors of a homogeneous matrix . Given integers and , we denote by the stratum of determinantal rings where are homogeneous of degrees .In this paper we extend previous results on the dimension and codimension of in to artinian determinantal rings, and we show that is generically smooth along under some assumptions. For zero and one dimensional determinantal schemes we generalize earlier results on these questions. As a consequence we get that the general element of a component W of the Hilbert scheme of is glicci provided W contains a standard determinantal scheme satisfying some conditions. We also show how certain ghost terms disappear under deformation while other ghost terms remain and are present in the minimal resolution of a general element of . 相似文献
3.
M. Carozza F. Giannetti A. Passarelli di Napoli C. Sbordone R. Schiattarella 《Journal of Mathematical Analysis and Applications》2018,457(2):1232-1246
In this paper we introduce the class of the inner p-quasiconformal mappings, that are homeomorphisms , , where is the unit disk, such that there exists a constant for which the following distortion inequalityis satisfied. The study of such mappings is motivated by the fact that their inverses satisfy the distortion inequality introduced in [11]. Here we give a characterization of them so that their components solve a suitable uniformly elliptic p-harmonic system. Moreover, for mappings satisfying the previous distortion inequality with not necessarily constant, we identify the homeomorphism f whose p-distortion function is minimal in norm. 相似文献
4.
5.
In this paper, we study operator-theoretic properties of the compressed shift operators and on complements of submodules of the Hardy space over the bidisk . Specifically, we study Beurling-type submodules – namely submodules of the form for θ inner – using properties of Agler decompositions of θ to deduce properties of and on model spaces . Results include characterizations (in terms of θ) of when a commutator has rank n and when subspaces associated to Agler decompositions are reducing for and . We include several open questions. 相似文献
6.
《Discrete Mathematics》2007,307(11-12):1430-1435
7.
8.
Cristhian E. Hidber Miguel A. Xicoténcatl 《Journal of Pure and Applied Algebra》2018,222(6):1478-1488
The purpose of this article is to compute the mod 2 cohomology of , the mapping class group of the Klein bottle with q marked points. We provide a concrete construction of Eilenberg–MacLane spaces and fiber bundles , where denotes the configuration space of unordered q-tuples of distinct points in and is the classifying space of the group . Moreover, we show the mod 2 Serre spectral sequence of the bundle above collapses. 相似文献
9.
Let D be a commutative domain with field of fractions K, let A be a torsion-free D-algebra, and let B be the extension of A to a K-algebra. The set of integer-valued polynomials on A is , and the intersection of with is , which is a commutative subring of . The set may or may not be a ring, but it always has the structure of a left -module.A D-algebra A which is free as a D-module and of finite rank is called -decomposable if a D-module basis for A is also an -module basis for ; in other words, if can be generated by and A. A classification of such algebras has been given when D is a Dedekind domain with finite residue rings. In the present article, we modify the definition of -decomposable so that it can be applied to D-algebras that are not necessarily free by defining A to be -decomposable when is isomorphic to . We then provide multiple characterizations of such algebras in the case where D is a discrete valuation ring or a Dedekind domain with finite residue rings. In particular, if D is the ring of integers of a number field K, we show that an -decomposable algebra A must be a maximal D-order in a separable K-algebra B, whose simple components have as center the same finite unramified Galois extension F of K and are unramified at each finite place of F. Finally, when both D and A are rings of integers in number fields, we prove that -decomposable algebras correspond to unramified Galois extensions of K. 相似文献
10.
11.
Vladimir Shchigolev 《Journal of Algebra》2009,321(5):1453-1462
12.
Douglas P. Hardin Michael C. Northington Alexander M. Powell 《Applied and Computational Harmonic Analysis》2018,44(2):294-311
A sharp version of the Balian–Low theorem is proven for the generators of finitely generated shift-invariant spaces. If generators are translated along a lattice to form a frame or Riesz basis for a shift-invariant space V, and if V has extra invariance by a suitable finer lattice, then one of the generators must satisfy , namely, . Similar results are proven for frames of translates that are not Riesz bases without the assumption of extra lattice invariance. The best previously existing results in the literature give a notably weaker conclusion using the Sobolev space ; our results provide an absolutely sharp improvement with . Our results are sharp in the sense that cannot be replaced by for any . 相似文献
14.
Anuj Jakhar Sudesh K. Khanduja Neeraj Sangwan 《Journal of Pure and Applied Algebra》2018,222(4):889-899
Let v be a Krull valuation of a field with valuation ring . Let θ be a root of an irreducible trinomial belonging to . In this paper, we give necessary and sufficient conditions involving only for to be integrally closed. In the particular case when v is the p-adic valuation of the field of rational numbers, and , then it is shown that these conditions lead to the characterization of primes which divide the index of the subgroup in , where is the ring of algebraic integers of K. As an application, it is deduced that for any algebraic number field K and any quadratic field L not contained in K, we have if and only if the discriminants of K and L are coprime. 相似文献
15.
16.
Dennis I. Merino 《Linear algebra and its applications》2012,436(7):1960-1968
17.
A Steiner 2- trade is a pair of disjoint partial Steiner triple systems, each on the same set of points, such that each pair of points occurs in if and only if it occurs in . A Steiner 2- trade is called d-homogeneous if each point occurs in exactly d blocks of (or ). In this paper we construct minimal d-homogeneous Steiner 2- trades of foundation and volume for sufficiently large values of . (Specifically, if is divisible by 3 and otherwise.) 相似文献
18.
19.