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 ...

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: 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 ...

“In mathematics, a Hilbert space is an inner product space that is complete with respect to the norm defined by the inner product. Hilbert spaces serve to clarify and generalize the concept of Fourier ...

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 This article has been retracted to straighten the academic record.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 ...

Abstract: We derive new bounds for the generalization error of kernel machines, such as support vector machines and related regularization networks by obtaining new ...