Related papers: Controlled frames in n-Hilbert spaces and their te…
We give a survey on classical and recent results on dual spaces of topological tensor products as well as some examples where these are used.
The study of controlled hybrid systems requires practical tools for approximation and comparison of system behaviors. Existing approaches to these problems impose undue restrictions on the system's continuous and discrete dynamics.…
We give a description of the image of tensor products of tautological bundles on Hilbert schemes of points on surfaces under the Bridgeland-King-Reid-Haiman equivalence. Using this, some new formulas for cohomological invariants of these…
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…
The main goal of this paper is to present new bounds for certain inner products in Hilbert spaces, with applications to the numerical radius and the operator norm. The obtained results significantly improve earlier results in this…
In the present paper the notion of continuous frames is introduced and some results of these frames are proved. Next, we give the concept of duals of continuous frames in Hilbert C*-modules and investigate some properties of them.
We introduce a novel data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system…
This paper mainly establishes the finite-horizon stochastic bounded real lemma, and then solves the $H_{\infty}$ control problem for discrete-time stochastic linear systems defined on the separable Hilbert spaces, thereby unifying the…
This paper generalizes results for alternate dual frames in Hilbert spaces on the situation of a Banach space. Additionally some properties of synthesys operator associated with alternate dual frame are investigated. The main result is that…
In this paper, we will introduce the concept of a continuous K-biframe for Hilbert spaces and we present various examples of continuous K-biframes. Furthermore, we investigate their characteristics from the perspective of operator theory by…
This paper considers the inversion of ill-posed linear operators. To regularise the problem the solution is enforced to lie in a non-convex subset. Theoretical properties for the stable inversion are derived and an iterative algorithm akin…
The characteristic stretching and squeezing of chaotic motion is linearized within the finite number of phase space domains which subdivide a classical baker map. Tensor products of such maps are also chaotic, but a more interesting…
We develop the theory of frames and Parseval frames for finite-dimensional vector spaces over the binary numbers. This includes characterizations which are similar to frames and Parseval frames for real or complex Hilbert spaces, and the…
A Hilbert space frame on $R^n$ is {\it scalable} if we can scale the vectors to make them a tight frame. There are known classifications of scalable frames. There are two basic questions here which have never been answered in any $R^n$:…
We give a few observations on different types of bounded operators on a topological vector space X and their relations with compact operators on X. In particular, we investigate when these bounded operators coincide with compact operators.…
Affiliated and normal operators in octonion Hilbert spaces are studied. Theorems about their properties and of related algebras are demonstrated. Spectra of unbounded normal operators are investigated.
We present an inequality for tensor product of positive operators on Hilbert spaces by considering the tensor product of operators as words on certain alphabets (i.e., a set of letters). As applications of the operator inequality and by a…
This paper examines the boundary controllability of a Timoshenko laminated beam system subject to Venttsel-type boundary conditions. The study focuses on a novel configuration in which three controls are applied solely at the boundary of…
As needed for the construction of rank $n$ continuous frames on a right quaternionic Hilbert space the so-called S-spectrum of a right quaternionic operator is studied. Using the S-spectrum, as for the case of complex Hilbert spaces, along…
Using techniques from the theory of von Neumann algebras, we propose a framework for addressing questions of controllability of bilinear systems on infinite dimensional Hilbert spaces. In the setup, we assume only that the drift and control…