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Multipliers between kernels of Toeplitz operators are characterised in terms of test functions (so-called maximal vectors for the kernels); these maximal vectors may easily be parametrised in terms of inner and outer factorizations.…
Twisted Toeplitz matrices constitute a generalization of Toeplitz matrices in the sense that the entries on each diagonal no longer need to be constant, but are given by the values of a continuous function on a partition of $[0,1]$. We…
The authors of the title proved an elegant identity expressing a Toeplitz determinant in terms of the Fredholm determinant of an infinite matrix which (although not described as such) is the product of two Hankel matrices. The proof used…
This paper studies the problem of selecting a submatrix of a positive definite matrix in order to achieve a desired bound on the smallest eigenvalue of the submatrix. Maximizing this smallest eigenvalue has applications to selecting input…
The authors derive a McShane identity for once-punctured super tori. Relying upon earlier work on super Teichm\"uller theory by the last two-named authors, they further develop the supergeometry of these surfaces and establish asymptotic…
In 1988 Boyle and Krieger defined sub-matrices for representation matrices of sofic shift. This paper presents some details of relations between integral sub-matrices and representation matrices. Besides, we express a new version of the…
This paper investigates spectral properties of certain classes of positive operators originated from different matrices appeared in linear complementarity problem. These positive operators play a crucial role in various areas of mathematics…
Many applications in applied mathematics and control theory give rise to the unique solution of a Sylvester-like matrix equation associated with an underlying structured matrix operator $f$. In this paper, we will discuss the solvability of…
We study linear preserver problems on the linear space of $n\times n$ Toeplitz matrices over the real field or the complex field. In particular, characterizations are given for linear preservers of rank one matrices and linear preservers of…
We prove a spatial Isomorphism between two spaces of matrix valued truncated Toeplitz operators.
We investigate truncated Toeplitz operators belonging to the Schatten ideals. We completely characterize such operators when they have an analytic symbol or belong to the ideal of Hilbert-Schmidt operators. We also study model spaces…
Let (RmR), (SmS) and (TmT) be Noetherian local rings sharing the same residue eld k and prime characteristic p > 0. We establish some formulas relating the h-function and s-multiplicity of the ber product R T S in terms of the h-functions…
In this work, we solve the fundamental problem of describing the coordinate transformations that preserve the upper triangular Toeplitz form of the given operator field. Surprisingly, this problem is closely related to the description of…
We study the spectral properties of flipped Toeplitz matrices of the form $H_n(f)=Y_nT_n(f)$, where $T_n(f)$ is the $n\times n$ Toeplitz matrix generated by the function $f$ and $Y_n$ is the $n\times n$ exchange (or flip) matrix having $1$…
The Neumann--Zagier matrices of an ideal triangulation are integer matrices with symplectic properties whose entries encode the number of tetrahedra that wind around each edge of the triangulation. They can be used as input data for the…
The results in the paper are related to the classification problem for invariant subspaces of multiplication operators in several variables. The main results consist of characterizations, in the two dimensional case, of ideals of…
In this paper we study the equations of the elimination ideal associated with $n+1$ generic multihomogeneous polynomials defined over a product of projective spaces of dimension $n$. We first prove a duality property and then make this…
We establish necessary and sufficient conditions for a semigroup identity to hold in the monoid of $n\times n$ upper triangular tropical matrices, in terms of equivalence of certain tropical polynomials. This leads to an algorithm for…
We consider path-connected sets of matrices and the induced paths between eigenvalues. We discuss the equivalence relation generated by these paths, and how it relates to the presence of higher multiplicity eigenvalues realized by the set.…
Extriangulated categories give a simultaneous generalization of triangulated categories and exact categories. In this paper, we study silting subcategories of an extriangulated category. First, we show that a silting subcategory induces a…