ABSTRACT: Applications of the generalization of Mazur-Orlicz theorem to concrete spaces are proved. Suitable moment problems are solved, as applications of extension theorems of linear operators with ...

Since $N^3 \neq 0$, it follows that the minimal polynomial of $N$ is $z^4$. _Exercise 2_ Similarly, the characteristic polynomial is $z^6$ and a quick computation ...

Abstract. In this paper, we consider three classes of bounded linear operators on a topological vector space with respect to three different topologies which are introduced by Troitsky. We obtain some ...

T^2(w, z) = T(z, 0) = (0, 0), it follows that $G(0, T) = V$. Therefore every vector in $\mathbb{C}^2$ is a generalized eigenvector of $T$. _Exercise 2_ The ...

Linear operators form the backbone of modern mathematical analysis and have become indispensable in characterising the behaviour of dynamical systems. At their core, these operators are functions that ...

Linear operators form the cornerstone of analysis in Banach spaces, offering a framework in which one can rigorously study continuity, spectral properties and stability. Banach space theory, with its ...

Compact and weakly compact operators on function spaces are studied. Those operators are characterized by properties of finitely additive set functions whose existence is guaranteed by Riesz ...

ABSTRACT: Short Retraction Notice The paper does not meet the standards of "Advances in Pure Mathematics". This article has been retracted to straighten the academic record. In making this decision ...