Advances in Operator Theory最新文献

We present some weighted norm inequalities of bounded adjointable operators on the Hilbert C*-modules. Further, we use the Cartesian decomposition to obtain the lower bounds of numerical radius inequality over Hilbert C*-module. And the existing inequalities of numerical radius on the Hilbert C*-modules are refined.

Sequences defining a weighted matrix geometric mean are investigated and their convergence speed is analyzed. The superlinear convergence of a weighted mean based on the Ando–Li–Mathias (ALM) construction is proved. A weighted Cheap mean is defined and conditions on the weights for linear or superlinear convergence of order at least three are provided.

In the paper we introduce new norm derivative mappings and the corresponding orthogonality relations induced by it. We show that this notion is useful in the characterization of inner product spaces, characterization of smooth Banach spaces, Birkhoff orthogonality. We prove also some useful computational formulations.

In this paper two classes of operators related to weakly p-compact and almost Dunford–Pettis sequences which will be called almost Dunford–Pettis p-convergent operators and weak almost p-convergent operators are studied. Some properties of Banach lattices, the weak Dunford–Pettis property of order p and the strong relatively compact Dunford–Pettis property of order p are characterized in terms of almost Dunford–Pettis p-convergent and weak almost p-convergent operators.

The aim of the paper is to characterize all quasi-parabolic operators and provide an integral representation to each quasi-parabolic operator on the Bergman space (A_{lambda }^2(D_n)). We explore some aspects of operator theoretic properties such as compactness, spectrum, common invariant subspaces and more. Further, we show that the collection of all quasi-parabolic operators forms a maximal commutative (C^*)-algebra. As a consequence, we provide integral representation for operators in the (C^*)-algebra generated by Toeplitz operators with essentially bounded quasi-parabolic defining symbols.

We study weakly compact multilinear operators. We prove a variant of Gantmacher’s weak compactness theorem for multilinear operators. We also present Lions–Peetre type results on weak compactness interpolation for multilinear operators. Furthermore, we provide an analogue of Persson’s result on interpolation of weakly compact operators under the assumption that the target Banach couple satisfies a certain weakly compact approximation property.

In the present paper, based on the so called degree of nondensifiability (DND), we introduce the concept of Banach–Mazur nondensifiability number of two given Banach spaces and prove that such a number is an optimal lower bound for the well known Banach–Mazur distance. For a given infinite dimensional Banach space, we also introduce a new constant. We demonstrate a relationship between this constant and the Banach–Mazur distance.

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.