Related papers: A Note on Carlier Inequality
Kinematical Hilbert space for Einstein-Cartan theory is constructed via von Neumann ideas of infinity-dimensional tensor product of Hilbert spaces. Field of comframe is considered as basic variable what is in contrast with standard…
Some new reverses of the Cauchy-Schwarz inequality in inner product spaces are presented in this paper.The results obtained here complement the recent work of the references.
We will formulate and prove a generalization of the isoperimetric inequality in the plane. Using this inequality we will construct an unitary space - and in consequence - an isomorphic copy of a separable infinite dimensional Hilbert space,…
We extend the theory of operator-valued frames (resp. bases), hence the theory of frames (resp. bases), for Hilbert spaces and Hilbert C*-modules, in two folds. This extension leads us to develop the theory of operator-valued frames (resp.…
In this paper, we establish Parseval identities and surprising new inequalities for weaving frames in Hilbert space, which involve scalar $\lambda\in\rs$. By suitable choices of $\lambda$, one obtains the previous results as special cases.…
Based on a new idea of factorization, we prove an improved discrete Rellich inequality and discuss its optimality. We also give a conjecture on improved higher order discrete Hardy-like inequalities and formulate an open problem for the…
In this paper we consider a new kind of inequality related to fractional integration, motivated by Gressman's paper. Based on it we investigate its multilinear analogue inequalities. Combining with the Gressman's work on multilinear…
Existing concentration bounds for bounded vector-valued random variables include extensions of the scalar Hoeffding and Bernstein inequalities. While the latter is typically tighter, it requires knowing a bound on the variance of the random…
We prove a new type of Poincar\'e inequality on abstract Wiener spaces for a family of probability measures which are absolutely continuous with respect to the reference Gaussian measure. This class of probability measures is characterized…
In this paper we investigate real convex-transitive Banach spaces X, which admit a 1-dimensional bicontractive projection P on X. Various mild conditions regarding the weak topology and the geometry of the norm are provided, which guarantee…
We investigate the possibility of improving the $p$-Poincar\'e inequality $\|\nabla_{\mathbb{H}^N} u\|_p \ge \Lambda_p \|u\|_p$ on the hyperbolic space, where $p>2$ and $\Lambda_p:=[(N-1)/p]^{p}$ is the best constant for which such…
The first named author introduced the notion of upper stability for metric spaces as a relaxation of stability. The motivation was a search for a new invariant to distinguish the class of reflexive Banach spaces from stable metric spaces in…
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.
We investigate properties of measures in infinite dimensional spaces in terms of Poincar\'e inequalities. A Poincar\'e inequality states that the $L^2$ variance of an admissible function is controlled by the homogeneous $H^1$ norm. In the…
In this work, a refinement of the Cauchy--Schwarz inequality in inner product space is proved. A more general refinement of the Kato's inequality or the so called mixed Schwarz inequality is established. Refinements of some famous numerical…
We introduce a measure of super weak noncompactness $\Gamma$ defined for bounded linear operators and subsets in Banach spaces that allows to state and prove a characterization of the Banach spaces which are subspaces of a Hilbert generated…
We show: 1) The existence of the first twisted Hilbert space that is not isomorphic to its dual; this solves a problem posed by Cabello in [Nonlinear centralizers in homology, Math. Ann. 358 (2014), no. 3-4, 779-798]. 2) The existence of a…
We obtain some sufficient conditions for the Central Limit Theorem for the random processes (fields) with values in the separable part of Holder space in the modern terms of majorizing (minorizing) measures, belonging to X.Fernique and…
In this note, we present a refinement of the well-known AM-GM inequality. We use this improved inequalty to establish corresponding inequalities on Hilbert space. We also give some refinements of the Kantorovich inequality.
To describe a set of functions, which forms a reflexive subspace B of the classical Banach space L a special function that characterizes their average integral growth is introduced. It is shown that this function essentially depends on the…