ACTA SCIENTIARUM MATHEMATICARUM最新文献

Let (mathbb {F}) be a field. We investigate the greatest possible dimension (t_n(mathbb {F})) for a vector space of n-by-n matrices with entries in (mathbb {F}) and in which every element is triangularizable over the ground field (mathbb {F}). It is obvious that (t_n(mathbb {F}) ge frac{n(n+1)}{2}), and we prove that equality holds if and only if (mathbb {F}) is not quadratically closed or (n=1), excluding finite fields with characteristic 2. If (mathbb {F}) is infinite and not quadratically closed, we give an explicit description of the solutions with the critical dimension (t_n(mathbb {F})), reducing the problem to the one of deciding for which integers (k in mathopen {[![}2,nmathclose {]!]}) all k-by-k symmetric matrices over (mathbb {F}) are triangularizable.

In this paper, we revisit a classical result of B. Aupetit and J. Zemánek, whose proof could benefit from additional details.

In this paper, we give refinements of the classical Pólya inequality for real numbers, finite-dimensional matrices, and (C^*)-algebras. Moreover, we correct some previously obtained versions of refinements of the Heinz and Pólya inequality and generalize and improve them for (C^*)-algebras.

We study the duality problem for the class of disjoint limited completely continuous operators. As consequence, we give a generalization of a result given in H’michane et al. (Operators Matrices 8:593599, 2014. https://doi.org/10.7153/oam-08-31) about the direct duality problem and we give the correct version of the result given in H’michane et al. (Operators Matrices 8:593599, 2014. https://doi.org/10.7153/oam-08-31) about the reciprocal duality problem for the class of limited completely continuous operators.

In this paper, we give sufficient conditions for functions defined on the (L^{p})-space on Damek–Ricci spaces, (1<ple 2), providing the weighted integrability of their Fourier–Helgason transforms. These results generalize a famous Titchmarsh’s theorem and Younis’ theorem, due to El Ouadih and Daher on Damek–Ricci spaces (El Ouadih and Daher in L C R Math Acad Sci Paris 359:675–685, 2021).

Consider the problem of computing a common solution to the simultaneous equations (Tx=x) and (Fx=x) in the framework of metric spaces. Nevertheless, if T is not a self-mapping and F is a self-mapping in particular, then it may be the case that the equation (Tx=x) has no solution and the equation (Fx=x) has a solution, in which case the system comprising the equations (Tx=x) and (Fx=x) is inconsistent. Eventually, it is of paramount interest and fundamental significance to identify a point in the space that serves as an approximate solution of the first equation (Tx=x), with the least possible error, and serves as an exact solution of the second equation (Fx=x). In view of the fact that for an approximate solution (x^{*}) of the equation (Tx=x), the quantum (d(x^{*}, Tx^{*})) scales the error due to approximation, one is conclusively interested in the constrained global minimization of the real valued error function (x longmapsto d(x, Tx)) subject to the constraint (Fx=x). The purpose of this paper is to resolve the preceding constrained global minimization problem in some special interesting cases, thereby generalizing some best proximity point theorems and fixed point theorems. It is remarked that unlike the preceding endeavor, the common best proximity point theorems accomplish unconstrained global minimization. Further, the results presented in this article generalize the most celebrated contraction principle due to Banach.

In this article, we investigate some important theoretical aspects of the deformed wavelet transform, which is a novel variant of the wavelet transform based on generalized translation and dilation operators governed by the well-known Dunkl transform. Besides studying all the fundamental properties, we establish the Calderón’s and inversion formulae associated with the newly proposed transform. Most importantly, we formulate a new class of localization operators associated with the deformed wavelet transform and examine the (L^p)-boundedness and compactness properties of such operators in detail.

We introduce the notion of local orthogonality preserving operators to study the right-symmetry of operators. As a consequence of our work, we show that any smooth compact operator defined on a smooth and reflexive Banach space is either a rank one operator or it is not right-symmetric. We show that there are no right-symmetric smooth compact operators defined on a smooth and reflexive Banach space that fails to have any non-zero left-symmetric point. We also study approximately orthogonality preserving and reversing operators (in the sense of Chmieliński and Dragomir). We show that on a finite-dimensional Banach space, an operator is approximately orthogonality reversing (preserving) in the sense of Dragomir if and only if it is close to a scalar multiple of an isometry.