Related papers: Bounded Power Series on the Real Line
We characterize the topologizability and power boundedness of convolution and dual convolution operators on power series spaces. We determine necessary conditions for a Toeplitz operator to be m-topologizable, and power bounded on…
Some boundedness properties of function spaces (considered as topological groups) are studied.
We define ''convergence'' for noncommutative power series and construct two topologies on the algebra of power series, convergent with respect to a positive radius. We indicate all finite dimensional continuous representations of this…
By the help of power series f we can naturally construct another power series that has as coefficients the absolute values of the coefficients of f. Utilising these functions we prove some inequalities for the spectral radius of the bounded…
We study topological boundedness of order-to-topology bounded and order-to-topology continuous operators from ordered vector spaces to topological vector spaces. The uniform boundedness principle for such operators is investigated.
Each series $\sum_{n=1}^\infty a_n$ of real positive terms gives rise to a topology on $\mathbb{N} = \{1,2,3,...\}$ by declaring a proper subset $A\subseteq \mathbb{N}$ to be closed if $\sum_{n\in A} a_n < \infty$. We explore the…
In this paper, we introduce statistical bounded set on topological vector space. Also, we consider three classes of bounded operators from topological vector spaces to ordered topological vector spaces. Moreover, we give relations between…
We construct an explicit filtration of the ring of algebraic power series by finite dimensional constructible sets, measuring the complexity of these series. As an application, we give a bound on the dimension of the set of algebraic power…
There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions…
Following several papers in the prior literature, we study the relationship between order bounded operators, topologically bounded operators and topologically continuous operators. Our main contribution is two folded: (i) we provide a set…
This paper studies boundedness and closedness of linear relations, which include both single-valued and multi-valued linear operators. A new (single-valued) linear operator induced by a linear relation is introduced, and its relationships…
In this paper, we explore a variety of series involving the central binomial coefficients, highlighting their structural properties and connections to other mathematical objects. Specifically, we derive new closed-form representations and…
The topology of a power grid affects its dynamic operation and settlement in the electricity market. Real-time topology identification can enable faster control action following an emergency scenario like failure of a line. This article…
Rational twisted power series over a (commutative) field are studied. We give several characterizations of such series, which are similar to the classical results concerning rational power series over a commutative field. In particular, we…
Rough set theory is an important mathematical tool for dealing with uncertain or vague information. This paper studies some new topologies induced by a binary relation on universe with respect to neighborhood opera- tors. Moreover, the…
Even in spaces of formal power series is required a topology in order to legitimate some operations, in particular to compute infinite summations. Many topologies can be exploited for different purposes. Combinatorists and algebraists may…
This paper is concerned with the convergence of power sequences and stability of Hilbert space operators, where "convergence" and "stability" refer to weak, strong and norm topologies. It is proved that an operator has a convergent power…
Let X, Y, and Z be topological modules over a topological ring $R$. In the first part of the paper, we introduce three different classes of bounded bigroup homomorphisms from $X\times Y$ into $Z$ with respect to the three different uniform…
In this note, we frst consider boundedness properties of a family of operators generalizing the Hilbert operator in the upper triangle case. In the diagonal case, we give the exact norm of these operators under some restrictions on the…
The contour of a family of filters along a filter is a set-theoretic lower limit. Topologicity and regularity of convergences can be characterized with the aid of the contour operation. Contour inversion is studied, in particular, for…