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Motivated by the famous Blanco-Koldobsky-Turn\v{s}ek characterization of isometries, we study the \textit{approximate preservation of Birkhoff-James orthogonality by a linear operator between Banach spaces}. In particular, we investigate…

We derive a lower and an upper bound for the rank of the finite part of operator $K$-theory groups of maximal and reduced $C^*$-algebras of finitely generated groups. The lower bound is based on the amount of polynomially growing conjugacy…

This is an introduction to the algebras $A\subset B(H)$ that the linear operators $T:H\to H$ can form, once a complex Hilbert space $H$ is given. Motivated by quantum mechanics, we are mainly interested in the von Neumann algebras, which…

We study Birkhoff-James orthogonality and isosceles orthogonality of bounded linear operators between Hilbert spaces and Banach spaces. We explore Birkhoff-James orthogonality of bounded linear operators in light of a new notion introduced…

We study classes of locally biholomorphic mappings defined in the $\P$ that have bounded Schwarzian operator in the Bergman metric. We establish important properties of specific solutions of the associated system of differential equations…

Real linear operators emerge in a range of mathematical physics applications. In this paper spectral questions of compact real linear operators are addressed. A Lomonosov-type invariant subspace theorem for antilinear compact operators is…

The class of stochastic maps, that is, linear, trace-preserving, positive maps between the self-adjoint trace class operators of complex separable Hilbert spaces plays an important role in the representation of reversible dynamics and…

This paper explores the Invariant Subspace Problem in operator theory and functional analysis, examining its applications in various branches of mathematics and physics. The problem addresses the existence of invariant subspaces for bounded…

Classes of homogeneous polynomials between Banach spaces have been studied in the last three decades from the perspective of the so-called ideal property: if a polynomial P belongs to a class Q, then the composition u o P o v of P with…

In this paper, we show that the essentiality of the scole of an ideal B i a semi-simple Banach algebra A implies that any invertibility preserving isomorphism on A is a Jordan homomorphism. Specially ...

In this paper semirings with an idempotent addition are considered. These algebraic structures are endowed with a partial order. This allows to consider residuated maps to solve systems of inequalities $A \otimes X \preceq B$. The purpose…

Prony's problem in several variables has attracted some attention recently and provides an interesting combination of polynomial ideal theory with analytic and numeric computations. This note points out further connections to Hankel…

In this note we study the structure of shift-preserving operators acting on a finitely generated shift-invariant space. We define a new notion of diagonalization for these operators, which we call s-diagonalization. We give necessary and…

In [CPPP] it was shown that Engel structures satisfy an existence $h$-principle, and the question of whether a full $h$-principle holds was left open. In this note we address the classification problem, up to Engel deformation, of Cartan…

Let A be a unital algebra over a commutative unital ring R. We say that A is a SLIP algebra if every R-linear map on A that leaves invariant every left ideal of A is a left multiplier. In this paper we study whether a triangular algebra…

In the present article we define and investigate relative Rota--Baxter operators and relative averaging operators on racks and rack algebras. Also, if B is a Rota--Baxter or averaging operator on a rack X, then we can extend B by linearity…

We introduce concepts of intermediate rank for countable groups that "interpolate" between consecutive values of the classical (integer-valued) rank. Various classes of groups are proved to have intermediate rank behaviors. We are…

Recently Yang-Roh-Jun introduced the notion of ordered BCI-algebras as a generalization of BCI-algebras. They also introduced the notions of homomorphisms and kernels of ordered BCI-algebras and investigated related properties. Here we…

In this paper we determine all the bijective linear maps on the space of bounded observables which preserve a fixed moment or the variance. Nonlinear versions of the corresponding results are also presented.

The concept of operator left residuation has been introduced by the authors in a previous paper. Modifications of so-called quantum structures, in particular orthomodular posets, like pseudo-orthomodular, pseudo-Boolean and Boolean posets…