Operators In Spaces Research Articles

ANY DUAL OPERATOR SPACE IS WEAKLY LOCALLY REFLEXIVE

Abstract We introduce the notion of weakly local reflexivity in operator space theory and prove that any dual operator space is weakly locally reflexive.

A new self-adaptive method for solving resolvent of sum of two monotone operators in Banach spaces

We introduce a Tseng extragradient method for solving monotone inclusion problem in Banach space. A strong convergence result of an Halpern inertial extrapolation method for solving the resolvent of sum of two monotone operators without the knowledge of the Lipschitz constant was established. Lastly, we illustrate some numerical behavior of our iterative scheme to showcase the performance of the proposed method compared to other related results in the literature.

Two regularized inertial Tseng methods for solving inclusion problems with applications to convex bilevel programming

Combining the inertial technique, regularization, and the Tseng method for approximating a zero of the sum of monotone operators in a real Hilbert space, we propose two regularized inertial Tseng methods for approximating a zero of the sum of two maximal monotone operators in the case where one of them is monotone and Lipschitz continuous. We establish strong convergence of the sequences generated by our algorithms and derive several interesting consequences of our results. We then apply our results to solving convex bilevel programming problems and illustrate the cost efficiency of our methods by numerically comparing them with other methods in the literature.

Tensorial and Hadamard product inequalities for functions of selfadjoint operators in Hilbert spaces in terms of Kantorovich ratio

Let H be a Hilbert space. In this paper we show among others that, if f, g are continuous on the interval I with 0 <γ ≤ f(t)/g(t)≤ Γ for t ∈ I and if A and B are selfadjoint operators with Sp (A), Sp (B) ⊂ I, then [f1−ν(A) gν (A)] ⊗ [fν(B) g1−ν (B)] ≤ (1 − ν) f (A) ⊗ g (B) + ν g (A) ⊗ f (B) ≤ [(γ + Γ) 2/4γΓ]R [f1−ν(A) gν (A)] ⊗ [fν(B) g1−ν (B)]. The above inequalities also hold for the Hadamard product “ ◦ ” instead of tensorial product “ ⊗ ”.

A limiting absorption principle for high-order Schrödinger operators in critical spaces

A limiting absorption principle for high-order Schrödinger operators in critical spaces

The Möbius addition and gyration operator in the octonionic space

The Möbius addition and gyration operator in the octonionic space

Directional Differentiability of the Metric Projection Operator in Uniformly Convex and Uniformly Smooth Banach Spaces

Directional Differentiability of the Metric Projection Operator in Uniformly Convex and Uniformly Smooth Banach Spaces

Quantum Time

A short introduction, with extended interpretations, to the Projection Evolution approach is presented. In this model time is like the other space positions represented by an operator in the state space of a physical system. As a pedagogigal example the Minkowski spacetime is considered. Finally, a short analysis of the time reversal symmetry is presented.

A Bilateral Teleoperation System With Learning-Based Cognitive Guiding Force

This article investigates the problem involving a fuzzy logic system-based bilateral teleoperation system with a unified impedance/admittance structure and learning-based assisted cognitive guiding force, enhancing a smooth transition between augmentation and autonomous motion on the master side. The impedance structure regulates the impedance and admittance via the parameters determined by the fuzzy logic system and, besides the variable impedance during interaction with the environment, the fuzzy Q-learning algorithm generates an assisted cognitive guiding force to guide the trainee operator in free space for reaching the interaction surface smoothly and steadily. The degeneration of tracking performance in the bilateral teleoperation system caused by time delay is analyzed and reduced via a mixed-type error. Experimental results verify the stability analyses, and under the proposed control scheme, the human-robot-environment interaction is smooth and stable.

Establishing “norms of behavior” for satellite collision avoidance maneuver planning

Several commercial companies, as well as various nations, have proposed to deploy or are deploying many satellites in Low Earth Orbit (LEO). These large constellations will greatly increase the number of satellites operating in relatively narrow altitude regions of space. The added space traffic in these regions will create many close approaches between the members of the large constellations and other space operators. These close approach situations can necessitate maneuver(s) to avoid a potential collision. Should both satellites have maneuvering capability, the question of how the overall collision avoidance procedures should be executed is raised. Some constellations may employ automated collision avoidance systems which interact differently than conventional human-in-the-loop systems. Interactions between an automated system and another operational satellite, between two automated systems or two nonautonomous systems present new challenges for executing effective collision avoidance. Additionally, the existence of non-maneuverable satellites and space debris continues to pose additional challenges. This paper is the first of several papers that will be documenting an International Academy of Astronautics study on this topic.

Spectrum of the Cesàro-Hardy operator in rearrangement invariant spaces

In this paper, we investigate the spectrum of the Cesàro-Hardy operator in rearrangement invariant spaces over a finite interval and a half line, thereby extending Boyd’s and Leibowitz’s results for Lp(1 < p ⩽ 8) spaces. In particular, when our rearrangement invariant space is the Lorentz space Lp,q , a full description of the spectrum and fine spectra is presented.

The Convergence of Some Spectral Characteristics on the Convergent Series

In this study, convergence properties of spectral, numerical and Crawford gap functions via convergences of Hilbert space operator series in difference and ratio cases are investigated. Obtained results have been applied to some classes continuous functions of the operators.

Generalized Euclidean operator radius

Abstract In this paper, we introduce the f-operator radius of Hilbert space operators as a generalization of the Euclidean operator radius and the q-operator radius. The properties of the newly defined radius are discussed, emphasizing how it extends some known results in the literature.

Construction of Intelligent Practice System of Visual Arts Based on VR Technology in Information Age

Abstract Taking visual art intelligence as an entry point, this paper describes the transformation brought by the information age to the expression of visual art. Based on VR technology to build a practice system of visual art intelligence, VR positioning technology is used to locate the three-dimensional coordinates of the operator in order to realize the independent positioning of multiple operators in a large space and avoid positioning interference. Through the eye movement multi-channel interaction algorithm based on head-eye synergy, the two-dimensional interaction task in flow field visualization is completed, and then gesture interaction is added to complete the three-dimensional interaction task. The constructed system was implemented in the teaching of art majors at College Z, and the data were analyzed. The results show that the total average scores of innovative theoretical ideas, interactive experience feeling, symbolic integration of creative content and infinite extension of the multidimensional spatial field are 82.42, 83.57, 80.84 and 80.28, respectively. The data show that teachers, students and parents recognize the intelligent system of visual arts and believe that it improves students’ innovative ability in art creation, enhances the interactive experience feeling of visual arts, and provides data support for the continuous research and exploration of contemporary visual arts.

Hierarchical neural architecture search with adaptive global–local feature learning for Magnetic Resonance Image reconstruction

Neural architecture search (NAS) has been introduced into the design of deep neural network architectures for Magnetic Resonance Imaging (MRI) reconstruction since NAS-based methods can acquire the complex network architecture automatically without professional designing experience and improve the model’s generalization ability. However, current NAS-based MRI reconstruction methods suffer from a lack of efficient operators in the search space, which leads to challenges in effectively recovering high-frequency details. This limitation is primarily due to the prevalent use of convolution operators in the current search space, which struggle to capture both global and local features of MR images simultaneously, resulting in insufficient information utilization. To address this issue, a generative adversarial network (GAN) based model is proposed to reconstruct the MR image from under-sampled K-space data. Firstly, parameterized global and local feature learning modules at multiple scales are added into the search space to improve the capability of recovering high-frequency details. Secondly, to mitigate the increased search time caused by the augmented search space, a hierarchical NAS is designed to learn the global–local feature learning modules that enable the reconstruction network to learn global and local information of MR images at different scales adaptively. Thirdly, to reduce the number of network parameters and computational complexity, the standard operations in global–local feature learning modules are replaced with lightweight operations. Finally, experiments on several publicly available brain MRI image datasets evaluate the performance of the proposed method. Compared to the state-of-the-art MRI reconstruction methods, the proposed method yields better reconstruction results in terms of peak signal-to-noise ratio and structural similarity at a lower computational cost. Additionally, our reconstruction results are validated through a brain tumor classification task, affirming the practicability of the proposed method. Our code is available at https://github.com/wwHwo/HNASMRI.

Some inequalities about Bourin's question in noncommutative L p -spaces

This paper studies a question of Bourin on noncommutative spaces. Some inequalities due to Hayajneh et al. [Norm inequalities for positive semidefinite matrices and a question of Bourin II. Int J Math. 2021;32:2150043] and Hayajneh et al. [Norm inequalities for positive semidefinite matrices and a question of Bourin III. Positivity. 2022;26:23] are extended to the case of operators in noncommutative spaces associated with a semifinite von Neumann algebra. We give a partial answer to a question of Bourin on noncommutative spaces. Some related submajorization inequalities are also given.

Classification of Ideals in Banach Spaces

Let an operator T belong to an operator ideal J, then for any operators A and B which can be composed with T asBTA then BTA \(\in\) J. Indeed, J contains the class of finite rank Banach Space operators. Now given L(X; Y ). Then J(X; Y ) \(\subseteq\) L(X; Y ) such that J(X; Y ) = {T : X \(\gets\) Y : T \(\subseteq\) }. Thus an operator ideal is a subclass J of L containing every identity operator acting on a one-dimensional Banach space such that: S + T \(\in\) J(X; Y ) where S; T \(\in\) J(X; Y ). If W;Z;X; Y \(\in\) K;A \(\in\) L(W;X);B \(\in\) L(Y;Z) then BTA \(\in\) J(W;Z) whenever T \(\in\) J(X; These properties compare very well with the algebraic notion of ideals in Banach Algebras within whose classes lie compact operators, weakly compact operators, finitely strictly regular operators, completely continuous operators, strictly singular operators among others. Thus, the aim of this paper is to characterize the various classes of ideals in Banach spaces. Special attention is given to the characteristics involving the ideal properties, the metric approximation properties, the hereditary properties in relation to the ideal extensions in the Hahn-Banach space, projection and embedments in the biduals of the Banach Space.

On Certain Spaces of Ideal Operators

We determine some important spaces of ideal operators and ideal characteristics. Special considerationis given to Frechet spaces, Spaces of finite rank operators and spaces of Hahn-Banach extension operators.The characteristics of ideals and related properties in these spaces as well as in some of their dual spacesare obtained.

Non-rough Norms and Dentability in Spaces of Operators

Non-rough Norms and Dentability in Spaces of Operators

Well‐posedness of degenerate fractional differential equations with finite delay in complex Banach spaces

AbstractWe study the well‐posedness of the degenerate fractional differential equations with finite delay: on Lebesgue–Bochner spaces and periodic Besov spaces , where and are closed linear operators in a complex Banach space satisfying , and are fixed, when , and the delay operator is a bounded linear operator from (resp. ) into . Using known operator‐valued Fourier multiplier theorems on and , we completely characterize the ‐well‐posedness and the ‐well‐posedness of above equations. We also give concrete examples that our abstract results may be applied.