Advances in Operator Theory最新文献

In this paper, we extend the basic idea of the Janashia–Lagvilava algorithm to adapt it for the spectral factorization of positive-definite polynomial matrices on the real line. This extension results in a new spectral factorization algorithm for polynomial matrix functions defined on (mathbb {R}). The presented numerical example demonstrates that the proposed algorithm outperforms an existing algorithm in terms of accuracy.

A characterization for the boundedness of multiplication and composition operators on Bloch type spaces is well-known. Wu, Zhao and Zorboska gave necessary and sufficient conditions for Toeplitz operators on Bloch type spaces to be bounded. In this paper, we discuss the boundedness of little Hankel operators with anti holomorphic symbols from a Bloch type space to an another Bloch type space.

Periodic Jacobi operators naturally arise in numerous applications, forming a cornerstone in various fields. The spectral theory associated with these operators boasts an extensive body of literature. Considered as discretized counterparts of Schrödinger operators, widely employed in quantum mechanics, Jacobi operators play a crucial role in mathematical formulations. The classical uniqueness result by G. Börg in 1946 occupies a significant place in the literature of inverse spectral theory and its applications. This result is closely intertwined with M. Kac’s renowned article, ‘Can one hear the shape of a drum?’ published in 1966. Since 1975,  discrete versions of Börg’s theorem have been available in the literature. In this article, we concentrate on the non-normal periodic Jacobi operator and the discrete versions of Börg’s Theorem. We extend recently obtained stability results to cover non-normal cases. The existing stability findings establish a correlation between the oscillations of the matrix entries and the size of the spectral gap. Our result covers the current self-adjoint versions of Börg’s theorem, including recent quantitative variations. Here, the oscillations of the matrix entries are linked to the path-connectedness of the pseudospectrum. Additionally, we explore finite difference approximations of various linear differential equations as specific applications.

The maximal hyperplane section of the (l_infty ^n)-ball, i.e. of the n-cube, is the one perpendicular to (frac{1}{sqrt{2}} (1,1,0 ,ldots ,0)), as shown by Ball. Eskenazis, Nayar and Tkocz extended this result to the (l_p^n)-balls for very large (p ge 10^{15}). By Oleszkiewicz, Ball’s result does not transfer to (l_p^n) for (2< p < p_0 simeq 26.265). Then the hyperplane section perpendicular to the main diagonal yields a counterexample for large dimensions n. Suppose that (p_0 le p < infty ). We show that the analogue of Ball’s result holds in (l_p^n)-balls for all hyperplanes with normal unit vectors a, if all coordinates of a have modulus (le frac{1}{sqrt{2}}) and p has distance (ge 2^{-p}) to the even integers. Under similar assumptions, we give a Gaussian upper bound for (20< p < p_0).

In this paper we present commutativity results for a general class of Szász–Mirakjan–Durrmeyer type operators and associated differential operators and investigate their eigenfunctions.Please confirm if the inserted city names are correct. Amend if necessary.The inserted city name is correct.

This paper is devoted to matrices with hyperbolical Krein space numerical range. This shape characterizes the 2-by-2 case and persists for certain classes of matrices, independently of their size. Necessary and sufficient conditions for low dimensional tridiagonal matrices to have this shape are obtained involving only the matrix entries.

We characterize the norm attainment set of a linear operator from ( ell _{infty }^{2}({mathbb {C}}) ) to ( ell _{1}^{2}({mathbb {C}}), ) with the help of a physical model involving two clocks entangled in a specific way. More generally, we introduce the (m, n)-clock Problem and establish its equivalence with computing the (ell _{infty }-ell _1) norm of an ( m times n ) matrix. We further give an explicit description of the smooth and the non-smooth points in ({mathbb {L}}big (ell _infty ^2({mathbb {C}}),ell _1^2({mathbb {C}})big ).)

In this study, singular value and norm inequalities for expressions of the form (SXT+Y) are established. It is shown that if (S,T,X,Y in mathcal {B(H)}) such that X, Y are compact operators, then

Additionally, we explore several applications of this inequality, which provide a broader framework for analysis and yield more nuanced insights. For (X, Yin mathcal {B(H)}) one notable application is the following inequality,

These results extend existing inequalities and offer new perspectives in operator theory.

Let X be a completely regular Hausdorff space and E and F be Banach spaces. Let (C_{rc}(X,E)) denote the Banach space of all continuous functions (f:Xrightarrow E) such that f(X) is a relatively compact set in E, and (beta _sigma ) be the strict topology on (C_{rc}(X,E)). We characterize dominated and absolutely summing operators (T:C_{rc}(X,E)rightarrow F) in terms of their representing operator-valued Baire measures. It is shown that every absolutely summing ((beta _sigma ,Vert cdot Vert _F))-continuous operator (T:C_{rc}(X,E)rightarrow F) is dominated. Moreover, we obtain that every dominated operator (T:C_{rc}(X,E)rightarrow F) is absolutely summing if and only if every bounded linear operator (U:Erightarrow F) is absolutely summing.

We investigate how continuous linear functionals can be represented in terms of generic operators and certain kernels (Peano kernels), and we study lower bounds for the operators as a consequence, in the space of square-integrable functions. We apply and develop the theory for the Riemann–Liouville fractional derivative (an inverse of the Riemann–Liouville integral), where inequalities are derived with the Gaussian hypergeometric function. This work is inspired by the recent contributions by Fernandez and Buranay (J Comput Appl Math 441:115705, 2024) and Jornet (Arch Math, 2024).