Related papers: An inequality for bi-orthogonal pairs
In this paper, we present several new bounds for the norm and numerical radius of sums of Hilbert space operators. The obtained bounds form a new collection that enriches our understanding of these bounds. We compare our bounds with the…
We study some examples when there is actually an equality in the linear algebra bound. When the vectors considered span in fact the entire space. We would like to point out that in some cases this provides some interesting extra information…
In this work we prove analogues of Bessel inequality and Riesz-Fisher theorem in Hilbert spaces with respect to sequences. We apply our generalized Bessel inequality to the Hilbert spaces associated with the Normal, Beta, Gamma and certain…
In this paper, structural properties of lower semi-frames in separable Hilbert spaces are explored with a focus on transformations under linear operators (may be unbounded). Also, the direct sum of lower semi-frames, providing necessary and…
We completely characterize Birkhoff-James orthogonality with respect to numerical radius norm in the space of bounded linear operators on a complex Hilbert space. As applications of the results obtained, we estimate lower bounds of…
We present some upper and lower bounds for the numerical radius of a bounded linear operator defined on complex Hilbert space, which improves on the existing upper and lower bounds. We also present an upper bound for the spectral radius of…
We prove lower bounds for the worst case error of quadrature formulas that use given sample points $\X_n = \{ x_1, \dots , x_n \}$. We are mainly interested in optimal point sets $\X_n$, but also prove lower bounds that hold with high…
We give an alternative lower bound for the numerical radii of Hilbert space operators. As a by-product, we find conditions such that \begin{equation*} \omega\left(\left[\begin{array}{cc} 0 & R \\ S & 0 \end{array}\right]\right)=\frac{\Vert…
We introduce an algebra model to study higher order sum rules for orthogonal polynomials on the unit circle. We build the relation between the algebra model and sum rules, and prove an equivalent expression on the algebra side for the sum…
Some elementary inequalities providing upper bounds for the difference of the norm and the numerical radius of a bounded linear operator on Hilbert spaces under appropriate conditions are given.
We slightly improve the lower bound of Baez-Duarte, Balazard, Landreau and Saias in the Nyman-Beurling formulation of the Riemann Hypothesis as an approximation problem. We construct Hilbert space vectors which could prove useful in the…
In this short note we present a far generalization of the following very well-known assertion: assume that we have two orthonormal sequences in a Hilbert space and these sequences are quadratically close to each other. Then if one of these…
We use the H\"{o}lder inequality for mixed exponents to prove some optimal variants of the generalized Hardy--Littlewood inequality for $m$-linear forms on $\ell _{p}$ spaces with mixed exponents. Our results extend recent results of Araujo…
In this work, a pre-Gr\"{u}ss inequality for positive Hilbert space operators is proved. So that, some numerical radius inequalities are proved. On the other hand, based on a non-commutative Binomial formula, a non-commutative upper bound…
Let $H$ be a real Hilbert space. In this short note, using some of the properties of bounded linear operators with closed range defined on $H$, certain bounds for a specific convex subset of the solution set of infinite linear…
We present a family of Bell inequalities for three parties and arbitrarily many outcomes, which can be seen as a natural generalization of the Mermin Bell inequality. For a small number of outcomes, we verify that our inequalities define…
We prove several singular value inequalities for sum and product of compact operators in Hilbert space. Some of our results generalize the previous inequalities for operators. Also, applications of some inequalities are given.
An approximation result for the bilinear Hilbert transform is proved and used for the inversion of the bilinear Hilbert transform. Also, p-Lebesgue points $(p\geq 1)$ are analyzed.
We give an expression for a generalized numerical radius of Hilbert space operators and then apply it to obtain upper and lower bounds for the generalized numerical radius. We also establish some generalized numerical radius inequalities…
The relationship between Salem numbers and short geodesics has been fruitful in quantitative studies of arithmetic hyperbolic orbifolds, particularly in dimensions 2 and 3. In this article, we push these connections even further. The…