Lacunary matrices

We study unconditional subsequences of the canonical basis e_rc of elementary matrices in the Schatten class S^p. They form the matrix counterpart to Rudin's Lambda(p) sets of integers in Fourier analysis. In the case of p an even integer, we find a sufficient condition in terms of trails on a bipartite graph. We also establish an optimal density condition and present a random construction of bipartite graphs. As a byproduct, we get a new proof for a theorem of Erdos on circuits in graphs.Comment: 14 page

New examples of noncommutative Λ(p) sets

This is a preprint of an article published in the Illinois Journal of Mathematics, vol.47 (2003), issue 4, pp.1063-1078.In this paper, we introduce a certain combinatorial property Z*(k), which is defined for every integer k ≥ 2, and show that every set E ⊂ Z with the property Z*(k) is necessarily a noncommutative Λ (2k) set. In particular, using number theoretic results about the number of solutions to so-called “S-unit equations,” we show that for any finite set Q of prime numbers, EQ is noncommutative Λ(p) for every real number 2 < p < ∞, where EQ is the set of natural numbers whose prime divisors all lie in the set Q

Short Kloosterman Sums for Polynomials over Finite Fields

This is a preprint of an article published in the Canadian Journal of Mathematics, 55 (2003), pp.225-246.We extend to the setting of polynomials over a finite field certain estimates for short Kloosterman sums originally due to Karatsuba. Our estimates are then used to establish some uniformity of distribution results in the ring Fq[x]/M(x) for collections of polynomials either of the form f−1g−1 or of the form f−1g−1 + afg, where f and g are polynomials coprime to M and of very small degree relative to M, and a is an arbitrary polynomial. We also give estimates for short Kloosterman sums where the summation runs over products of two irreducible polynomials of small degree. It is likely that this result can be used to give an improvement of the Brun-Titchmarsh theorem for polynomials over finite fields

Matrix inequalities with applications to the theory of iterated kernels

NOTICE: this is the author's version of a work that was accepted for publication in Linear Algebra and its Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Linear Algebra and its Applications, Volume 362 (2003), pp.275-286. doi:10.1016/S0024-3795(02)00517-7. http://www.elsevier.com/locate/laa.For an m × n matrix A with nonnegative real entries, Atkinson, Moran and Watterson proved the inequality s(A)3 ≤ mns(AAtA), where At is the transpose of A, and s(·) is the sum of the entries. We extend this result to finite products of the form AAtAAt . . .A or AAtAAt . . .At and give some applications to the theory of iterated kernels

Dicaesium magnesium bis­(dihydrogen phosphate(V)) dihydrate

The title compound, Cs2Mg(H2P2O7)2·2H2O, is isostructural with the related known isoformular phosphates. The crystal framework consists of corner-sharing MgO6 and H2P2O7 polyhedra, leading to tunnels parallel to the b-axis direction in which Cs+ ions are located. The H2P2O7 unit shows a bent eclipsed conformation. The Mg2+ ion lies on an inversion center. The water molecules form hydrogen bonds to O atoms of two different dihydrogenphosphate ions, which are further hydrogen bonded to symmetry-equivalent dihydrogenphosphate ions

Vibrational analysis of Ag3(PO2NH)3, Na3(PO2NH)3.H2O, Na3(PO2NH)3.4H2O, [C(NH2)3]3(PO2NH)3.H2O and (NH4)4(PO2NH)4.4H2O

FT IR and FT Raman spectra of Ag3(PO2NH), (Compound I), Na3(PO2NH)3.H2O (Compound II), Na3(PO2NH)3.4H2O (Compound III), [C(NH2)3]3(PO2NH)3.H2O (Compound IV) and (NH4)4(PO2NH)4.4H2O (Compound V) are recorded and analyzed on the basis of the anions, cations and water molecules present in each of them. The PO2NH− anion ring in compound I is distorted due to the influence of Ag+ cation. Wide variation in the hydrogen bond lengths in compound III is indicated by the splitting of the v2 and v3 modes of vibration of water molecules. The NH4 ion in compound V occupies lower site symmetry and exhibits hindered rotation in the lattice. The correlations between the symmetric and asymmetric stretching vibrations of P-N-P bridge and the P-N-P bond angle have also been discussed

Noncommutative Figa-Talamanca-Herz algebras for Schur multipliers

We introduce a noncommutative analogue of the Fig\'a-Talamanca-Herz algebra $A_p(G)$ on the natural predual of the operator space $\frak{M}_{p,cb}$ of completely bounded Schur multipliers on Schatten space $S_p$. We determine the isometric Schur multipliers and prove that the space $\frak{M}_{p}$ of bounded Schur multipliers on Schatten space $S_p$ is the closure in the weak operator topology of the span of isometric multipliers.Comment: 24 pages; corrected typo

Fourier analysis, Schur multipliers on SpS^p and non-commutative Λ(p)-sets

This work deals with various questions concerning Fourier multipliers on $L^p$, Schur multipliers on the Schatten class $S^p$ as well as their completely bounded versions when $L^p$ and $S^p$ are viewed as operator spaces. For this purpose we use subsets of ℤ enjoying the non-commutative Λ(p)-property which is a new analytic property much stronger than the classical Λ(p)-property. We start by studying the notion of non-commutative Λ(p)-sets in the general case of an arbitrary discrete group before turning to the group ℤ