Related papers: On the Pelczynski conjecture on Auerbach Bases

In the paper, results on the existence of critical points in annular subsets of a cone are obtained with the additional goal of obtaining multiplicity results. Compared to other approaches in the literature based on the use of…

We consider a generalized Baernstein space associated to a compact family of finite subsets of an uncountable set. We show that for certain transfinitely defined families such spaces admit an equivalent $2$-rotund norm. We also show that…

We prove a general result on complemented unconditional basic sequences in Banach lattices and apply it to give some new examples of spaces with unique unconditional basis. We show that Tsirelson space and certain Nakano spaces have the…

A complete set of N+1 mutually unbiased bases (MUBs) exists in Hilbert spaces of dimension N = p^k, where p is a prime number. They mesh naturally with finite affine planes of order N, that exist when N = p^k. The existence of MUBs for…

Let X be a compact Riemann surface together with a finite set of marked points. We use Morse theoretic techniques to compute the Betti numbers of the parabolic U(2,1)-Higgs bundles moduli spaces over X. We give examples for one marked point…

Continuing [5], this paper investigates finer points of supertropical vector spaces, including dual bases and bilinear forms, with supertropical versions of standard classical results such as the Gram-Schmidt theorem and Cauchy-Schwarz…

We develop a strong connection between maximally commuting bases of orthogonal unitary matrices and mutually unbiased bases. A necessary condition of the existence of mutually unbiased bases for any finite dimension is obtained. Then a…

We show that the Hurwitz problem for sums of squares can depend on the base field. More precisely, we construct an explicit formula of type $[12,12,18]$ over every field of characteristic different from $2$ in which $-1$ is a square,…

We relate the construction of a complete set of cyclic mutually unbiased bases, i. e., mutually unbiased bases generated by a single unitary operator, in power-of-two dimensions to the problem of finding a symmetric matrix over F_2 with an…

The question of determining the maximal number of mutually unbiased bases in dimension six has received much attention since their introduction to quantum information theory, but a definitive answer has still not been found. In this paper…

The space of Bloch functions on bounded symmetric domains is extended by considering Bloch functions $f$ on the unit ball $B_E$ of finite and infinite dimensional complex Banach spaces in two different ways: by extending the classical Bloch…

We give a sufficient criterion for complex analyticity of nonlinear maps defined on direct limits of normed spaces. This tool is then used to construct new classes of (real and complex) infinite dimensional Lie groups: (a) groups of germs…

We shall present a new characterization of greedy bases and 1-greedy bases in terms of certain functionals defined using distances to one dimensional subspaces generated by the basis. We also introduce a new property that unifies the…

We introduce the concept of strategically reproducible bases in Banach spaces and show that operators which have large diagonal with respect to strategically reproducible bases are factors of the identity. We give several examples of…

A broader class of Hardy spaces and Lebesgue spaces have been introduced recently on the unit circle by considering continuous $\|.\|_1$-dominating normalized gauge norms instead of the classical norms on measurable functions and a Beurling…

We use geometrical combinatorics arguments, including the ``hairbrush'' and x-ray arguments of Wolff and the sticky/plany/grainy analysis of Katz, Laba, and Tao, to show that Besicovitch sets in R^n have Minkowski dimension at least (n+2)/2…

We prove stronger variants of a multiplier theorem of Kislyakov. The key ingredients are based on ideas of Kislaykov and the Kahane-Salem-Zygmund inequality. As a by-product we show various multiplier theorems for spaces of trigonometric…

We classify the first few brane tilings on a genus 2 Riemann surface and identify their toric Calabi-Yau moduli spaces. These brane tilings are extensions of tilings on the 2-torus, which represent one of the largest known classes of 4d N=1…

In this paper, first we present a new useful way of formulating probabilistic normed spaces. Then by using this formulation and probabilistic normed space version of the Baire category theorem, we prove four important results of functional…

It was proved by Argyros and Dodos that, for many classes $ C $ of separable Banach spaces which share some property $ P $, there exists an isomorphically universal space that satisfies $ P $ as well. We introduce a variant of their…