Related papers: A generic transformation is invertible

Let $F$ be an ordered topological vector space (over $\mathbb{R}$) whose positive cone $F_+$ is weakly closed, and let $E \subseteq F$ be a subspace. We prove that the set of positive continuous linear functionals on $E$ that can be…

A generalization with singular weights of Moore-Penrose generalized inverses of closed range operators in Hilbert spaces is studied using the notion of compatibility of subspaces and positive operators.

In this paper, we show that the generalized Aluthge transforma- tions of a large class of operators (weighted conditional type operators) are normal. As a consequence, the operator MwEMu is p-hyponormal if and only if it is normal, and…

The generalized Jacobi equation is a differential equation in local coordinates that describes the behavior of infinitesimally close geodesics with an arbitrary relative velocity. In this note we study some transformation properties for…

Invertibility of Toeplitz operators on the Bergman space and the related Douglas problem are long standing open problems. In this paper we study the invertibility problem under the novel geometric condition on the image of the symbols,…

We show that any unitary transformation performed on the quantum state of a closed quantum system, describes an inner, reversible, generalized quantum measurement. We also show that under some specific conditions it is possible to perform a…

We prove that any bijective fidelity preserving transformation on the set of all density operators on a Hilbert space is implemented by an either unitary or antiunitary operator on the underlying Hilbert space.

We study coinductive invertibility of cells in weak $\omega$-categories. We use the inductive presentation of weak $\omega$-categories via an adjunction with the category of computads, and show that invertible cells are closed under all…

We first give a condition for a normal operator on a Hilbert space to have no nonzero periodic points, then we give a characterization of normal operators with the whole space as periodic points. We proceed to study the structure of…

We give an introductory account of the recently identified gauge invariance of the equilibrium statistical mechanics of classical many-body systems [J. M\"uller et al., Phys. Rev. Lett. Phys. Rev. Lett. 133, 217101 (2024)]. The gauge…

For irreducible interval exchange transformations, we study the relation between the powers of induced map and the induced maps of powers and raise a condition of equivalence between them. And skew production of Rauzy induction map is set…

Quantum measurements can be interpreted as a generalisation of probability vectors, in which non-negative real numbers are replaced by positive semi-definite operators. We extrapolate this analogy to define a generalisation of doubly…

We consider generalized gradients in the general context of $G$-structures. They are natural first order differential operators acting on sections of vector bundles associated to irreducible $G$-representations. We study their geometric…

A construction of conservation laws for $\sigma$-models in two dimensions is generalized in the framework of noncommutative geometry of commutative algebras. This is done by replacing the ordinary calculus of differential forms with other…

We consider a higher-derivative generalization of disformal transformations in $D$-dimensional spacetime and clarify the conditions under which they form a group with respect to the matrix product and the functional composition. These…

Let $\mathbb{P}$ be the complete metric space consisting of positive invertible operators on an infinite-dimensional Hilbert space with the Thompson metric. We introduce the notion of operator means of probability measures on $\mathbb{P}$,…

We construct a normal countably tight $T_1$ space $X$ with $t(X_\delta) >2^\omega$. This is an answer to the question posed by Dow-Juh\'asz-Soukup-Szentmikl\'ossy-Weiss. We also show that if the continuum is not so large, then the tightness…

We utilize Gaussian measure preserving systems to prove the existence and genericity of Lebesgue measure preserving transformations $T:[0,1]\rightarrow [0,1]$ which exhibit both mixing and rigidity behavior along families of asymptotically…

In a large class of statistical inverse problems it is necessary to suppose that the transformation that is inverted is known. Although, in many applications, it is unrealistic to make this assumption, the problem is often insoluble without…

Any deterministic autonomous dynamical system may be globally linearized by its' Koopman operator. This object is typically infinite-dimensional and can be approximated by the so-called Dynamic Mode Decomposition (DMD). In DMD, the central…