Related papers: Atomic subspaces for operators
Fusion reactions below the Coulomb barrier provide new insights into multidimensional quantum tunneling, nuclear reaction dynamics and nuclear structure. These reactions are also of considerable interest to nuclear astrophysics. In this…
We describe the proper closed invariant subspaces of the integration operator when it acts continuously on countable intersections and countable unions of weighted Banach spaces of holomorphic functions on the unit disc or the complex…
The multiple-quantum NMR spectroscopy has an extensive application in determination of the bio-macro-molecular structures and in the investigation of the properties of a variety of physical materials. In quantum computation the…
Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums,where the harmonic sums and their…
We establish the various properties as well as diverse relations of the ascent and descent spectra for bounded linear operators. We specially focus on the theory of subspectrum. Furthermore, we construct a new concept of convergence for…
In this paper we will look at the connection of frames and finite dimensionality. A main focus is to present simple algorithms and make them available online. The main result is a way to 'switch' between different frames, giving an…
A finite-dimensional Hilbert space is usually described in terms of an orthonormal basis, but in certain approaches or applications a description in terms of a finite overcomplete system of vectors, called a finite tight frame, may offer…
We define a notion of formal quantum field theory and associate a formal quantum field theory to K-theoretical intersection theories on Hilbert schemes of points on algebraic surfaces. This enables us to find an effective way to compute…
This chapter offers a detailed survey on intrinsically localized frames and the corresponding matrix representation of operators. We re-investigate the properties of localized frames and the associated Banach spaces in full detail. We…
Unitary operators are essential to quantum mechanics, however for discrete systems larger than a qubit, it is difficult to express them in a self-contained way. This report presents just such a description, providing a compact, useful…
Transmitted data may be corrupted by both noise and data loss. Grassmannian frames are in some sense optimal representations of data transmitted over a noisy channel that may lose some of the transmitted coefficients. Fusion frame (or frame…
We derive atomic decompositions and frames for weighted Bergman spaces of several complex variables on the unit ball in the spirit of Coifman, Rochberg, and Luecking. In contrast to our predecessors, we use group theoretic methods, in…
Relativistic dynamics with energy and momentum resricted to an anti-de-Sitter space is presented, specifically in the introduction of coordiate operators conjugate to such momenta. Definition of functions of these operators, their…
Composite quantum systems can be decomposed into subsystems in many different inequivalent ways. We call a particular decomposition a meronomic reference frame for the system. We apply the ideas of quantum reference frames to characterize…
Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…
In this talk I review various notions of generalised global symmetry: higher-form, higher-group, and non-invertible symmetry. All these notions have had profound impact on quantum field theory research in the last decade. I highlight…
In this paper, we quantize universal gauge groups such as SU(\infty), as well as their homogeneous spaces, in the sigma-C*-algebra setting. More precisely, we propose concise definitions of sigma-C*-quantum groups and sigma-C*-quantum…
An operator generalisation of the notion of geometric phase has been recently proposed purely based on physical grounds. Here we provide a mathematical foundation for its existence, while uncovering new geometrical structures in quantum…
This paper has a twofold purpose: to present an overview of the theory of absolutely summing operators and its different generalizations for the multilinear setting, and to sketch the beginning of a research project related to an objective…
In this papers we investigate the g-frame and Bessel g-sequence related to a linear bounded operator $K$ in Hilbert $C^{\ast}$-module and we establish some results.