Related papers: Modular Deutsch Entropic Uncertainty Principle

We introduce and study some new uniform structures for Hilbert $C^*$-modules over an algebra $A$. In particular, we prove that in some cases they have the same totally bounded sets. To define one of them, we introduce a new class of…

The Heisenberg uncertainty principle is one of the fundamental pillars of quantum mechanics and quantum field theory. It is normally introduced by postulating the commutation relations $[\hat{x}^i, \hat{p}^j] = i\hbar \delta^{ij}$. However,…

Analogues for Hilbert C*-modules of classical results of Fourier series theory in Hilbert spaces are considered. Relations between different properties of orthogonal and orthonormal systems for Hilbert C*-modules are studied with special…

We prove a covariant version of the Stinespring theorem for Hilbert C*-modules.

We investigate complexes of Hilbert C*-modules, which are cochain complexes with (unbounded) regular operators between Hilbert C*-modules as differential maps. In particular, we provide various equivalent characterizations of the Fredholm…

The H$\ddot{{\rm o}}$lder-McCarty inequalities are originally derived in the Hilbert space case and have been generalized via a convex inequality. The main purpose of this paper is to extend this convex inequality to the Hilbert…

We construct an example of a Hilbert C*-module which shows that Troitsky's theorem on the geometrical essence of A-compact operators between Hilbert C*-modules is not extendable to a not countably generated module case (even in the case of…

In this paper, we uncover a new uncertainty principle that governs the complexity of Boolean functions. This principle manifests as a fundamental trade-off between two central measures of complexity: a combinatorial complexity of its…

In this article we survey some of the recent goings-on in the classification programme of C$^*$-algebras, following the interesting link found between the Cuntz semigroup and the classical Elliott invariant and the fact that the Elliott…

In this paper we uses an I.I. Hirschman-W. Beckner entropy argument to give an uncertainty inequality for the $q$-Bessel Fourier transform: $$ \mathcal{F}_{q,v}f(x)=c_{q,v}\int_{0}^{\infty}f(t)j_{v}(xt,q^{2})t^{2v +1}d_{q}t, $$ where…

The aim of this paper is to prove a logarithmic and a Hirschman-Beckner entropic uncertainty principles for the Hankel wavelet transform. Then we derive a general form of Heisenberg-type uncertainty inequality for this transformation.

We analyze entropic uncertainty relations in a finite dimensional Hilbert space and derive several strong bounds for the sum of two entropies obtained in projective measurements with respect to any two orthogonal bases. We improve the…

We show that quantum entanglement and the Heisenberg uncertainty principle are inextricably connected. Toward this end, a complete set of commuting observables (CSCO) criterion for the entanglement is developed. Assuming (A1,A2,...) and…

For the power-law quantum wave packet in configuration space, the variance of the position observable may be divergent. Accordingly, the information-entropic formulation of the uncertainty principle becomes more appropriate than the…

A new approach to the Lance-Blecher theorem is presented resting on the interpretation of elements of Hilbert C*-module theory in terms of multiplier theory of operator C*-algebras: The Hilbert norm on a Hilbert C*-module allows to recover…

We study the notions of nuclearity and exactness for module maps on $C^{*}$-algebras which are $C^*$-module over another $C^*$-algebra with compatible actions and examine finite approximation properties of such $C^*$-modules. We prove…

We consider several natural ways of expressing the idea that a one-sided ideal in a C*-algebra (or a submodule in a Hilbert C*-module) is large, and show that they differ, unlike the case of two-sided ideals in C*-algebras. We then show how…

The aim of this paper is establish the Heisenberg-Pauli-Weyl uncertainty principle and Donho-Stark's uncertainty principle for the Weinstein $L^2$-multiplier operators.

We prove stability theorems in the Cuntz semigroup of a commutative C*-algebra which are analogues of classical stability theorems for topological vector bundles over compact Hausdorff spaces. Several applications to simple unital AH…

We prove several versions of reverse triangle inequality in Hilbert $C^*$-modules. We show that if $e_1, ..., e_m$ are vectors in a Hilbert module ${\mathfrak X}$ over a $C^*$-algebra ${\mathfrak A}$ with unit 1 such that $<e_i,e_j>=0…