Related papers: Simultaneous generic approximation by the iterates…
The sets of strongly supercyclic, weakly l-sequentially supercyclic, weakly sequentially supercyclic, and weakly supercyclic vectors for an arbitrary normed-space operator are all dense in the normed space, regardless the notion of…
A regular generalized sampling theory in some structured T-invariant subspaces of a Hilbert space H, where T denotes a bounded invertible operator in H, is established in this paper. This is done by walking through the most important cases…
A commutative associative algebra A with an identity over the field of real numbers which has a basis, where all elements are invertible, is considered in the work. Moreover, among matrixes consisting of the structure constants of A, there…
The Ces\`aro limit - the asymptotic average of a sequence of real numbers - is an operator of fundamental importance in probability, statistics and analysis. Surprisingly, spaces of sequences with Ces\`aro limits have not previously been…
Georgiou, Katkov and Tsodyks considered the following random process. Let $x_1,x_2,\ldots $ be an infinite sequence of independent, identically distributed, uniform random points in $[0,1]$. Starting with $S=\{0\}$, the elements $x_k$ join…
The Kolakoski sequence is the unique infinite sequence with values in $\{1,2\}$ and first term $1$ which equals the sequence of run-lengths of itself, we call this $K(1,2).$ We define $K(m,n)$ similarly. A well-known conjecture is that the…
In this work, we investigate k-nearly uniform convex(k-NUC) and the uniform Opial properties of the sequence space defined by de la Vallee-Poussin mean. Also we give some corollaries concerning the geometrical properties of this space.
We study binomially weighted summation methods given by \[ (x_n)_{n\in \mathbb{N}} \mapsto \left(\sum_{k=0}^n\binom{n}{k}r^k(1-r)^{n-k}x_k\right)_{n\in \mathbb{N}} \] for $r\in (0,1)$, and their behavior under composition with summation…
Let L be a finite extension of Qp, and let K be a spherically complete non-archimedean extension field of L. In this paper we introduce a restricted category of continuous representations of locally L-analytic groups G in locally convex…
In this Letter we make progress on a longstanding open problem of Aaronson and Ambainis [Theory of Computing 1, 47 (2005)]: we show that if A is the adjacency matrix of a sufficiently sparse low-dimensional graph then the unitary operator…
On a separable C*-algebra A every (completely) bounded map, which preserves closed two sided ideals, can be approximated uniformly by elementary operators if and only if A is a finite direct sum of C*-algebras of continuous sections…
Let $T$ be a power bounded Hilbert space operator without unimodular eigenvalues. We show that the subsequential ergodic averages $N^{-1}\sum_{n=1}^N T^{a_n}$ converge in the strong operator topology for a wide range of sequences $(a_n)$,…
The aim of the current paper is to determine the necessary and sufficient conditions for the weights $\mathbf{q}=\{q_k\}$, ensuring that the sequence of operators $\left\{ T_{n}^{\left( \mathbf{q}\right) }f\right\} $ associated with Walsh…
We show topological genericity for the set of functions in the space X, where X denotes the intersection of the Hardy spaces H^p with p<1, on the open unit disc such that the sequence of Taylor coefficients of the function and of all…
Let $S$ be a finite set with $n$ elements in a real linear space. Let $\cJ_S$ be a set of $n$ intervals in $\nR$. We introduce a convex operator $\co(S,\cJ_S)$ which generalizes the familiar concepts of the convex hull $\conv S$ and the…
We study real and complex interpolation of abstract Ces\`aro, Copson and Tandori spaces, including the description of Calder\'on-Lozanovski{\v \i} construction for those spaces. The results may be regarded as generalizations of…
For $c\in(1,2)$ we consider the following operators \[ \mathcal{C}_{c}f(x) = \sup_{\lambda \in [-1/2,1/2)}\bigg| \sum_{n \neq 0}f(x-n) \frac{e^{2\pi i\lambda \lfloor |n|^{c} \rfloor}}{n}\bigg|\text{,}\quad \mathcal{C}^{\mathsf{sgn}}_{c}f(x)…
In this paper we prove Korovkin type theorem for iterates of general positive linear operators $T:C\left[ 0,1\right] \rightarrow C\left[ 0,1\right] $ and derive quantitative estimates in terms of modulus of smoothness. In particular, we…
We show that if $V$ is a vertex operator algebra such that all the irreducible ordinary $V$-modules are $C_1$-cofinite and all the grading-restricted generalized Verma modules for $V$ are of finite length, then the category of finite length…
Generic computability has been studied in group theory and we now study it in the context of classical computability theory. A set A of natural numbers is generically computable if there is a partial computable function f whose domain has…