Rotundity and monotonicity properties of selected Cesàro function spaces

Positivity - We study rotundity, strict monotonicity, lower local uniform monotonicity and upper local uniform monotonicity in some classes of Cesàro function spaces. We present full criteria...     

Multiplication operators on Cesàro second order function spaces

Positivity - In this article, we investigate bounded, invertible and compact multiplication operators on the second order Cesàro function spaces.     

Spectral properties of generalized Cesàro operators on Hardy and weighted Bergman spaces

We investigate spectral properties of integral operators of the form

Convolution operators in discrete Cesàro spaces

Archiv der Mathematik - The discrete Cesàro spaces $${{\text {ces(p )}}}, 1< p < \infty ,$$ are well known and arise from the classical sequence spaces $$\ell ^p,1<\infty...     

Mean ergodicity and spectrum of the Cesàro operator on weighted $$c_0$$ spaces

A detailed investigation is made of the continuity, the compactness and the spectrum of the Cesàro operator \(\mathsf {C}\) acting on the weighted Banach sequence space \(c_0(w)\) for a bounded, strictly positive weight w. New features arise in the weighted setting (e.g. existence of eigenvalues, compactness, mean ergodicity) which are not present in the classical setting of \(c_0\).     

Extended Cesàro Operators between Different Bergman

In this paper, we obtain the characterizations onμ for (p, q) - φ Carleson measure,different weighted Bergman spaces as some application.     

On weighted uniform Cesàro summability of Jacobi-Fourier series

The aim of this paper is to give weighted function spaces in which the sequence of Cesàro means of the Jacobi-Fourier series are uniformly convergent. Error estimate for the approximation will also be considered.     

Factorization of Cesàro and Hilbert matrices based on generalized Cesàro matrix

ABSTRACT

In this paper, we introduce factorizations for the Hilbert and Cesàro matrices based on generalized Cesàro matrix and as the application, we generalize the Hardy's inequality versus Hilbert's.     

Isomorphic copies of $$l^\infty $$ in Cesàro–Orlicz function spaces

We characterize Cesàro–Orlicz function spaces \(Ces_\varphi \) containing isomorphic copy of \(l^\infty \). We also describe the subspaces \((Ces_\varphi )_a\) of all order continuous elements of \(Ces_\varphi \). Finally, we study the monotonicity structure of the spaces \(Ces_\varphi \) and \((Ces_\varphi )_a\).     

On Cesàro summability of vector valued multiplier spaces and operator valued series

In this paper, we introduce and study vector valued multiplier spaces with the help of the sequence of continuous linear operators between normed spaces and Cesàro convergence. Also, we obtain a new version of the Orlicz–Pettis Theorem by means of Cesàro summability.     

Absolute Cesàro Series Spaces and Matrix Operators

In this paper we derive a series space \(\vert C_{\lambda,\mu} \vert _{k}\) using the well known absolute Cesàro summability \(\vert C_{\lambda,\mu} \vert _{k}\) of Das (Proc. Camb. Philol. Soc. 67:321–326, 1970), compute its \(\beta\)-dual, give some algebraic and topological properties, and characterize some matrix operators defined on that space. So we generalize some results of Bosanquet (J. Lond. Math. Soc. 20:39–48, 1945), Flett (Proc. Lond. Math. Soc. 7:113–141, 1957), Mehdi (Proc. Lond. Math. Soc. (3)10:180–199, 1960), Mazhar (Tohoku Math. J. 23:433–451, 1971), Orhan and Sar?göl (Rocky Mt. J. Math. 23(3):1091–1097, 1993) and Sar?göl (Commun. Math. Appl. 7(1):11–22, 2016; Math. Comput. Model. 55:1763–1769, 2012).     

Point spectra of Cesàro matrices

For all positive a the point spectrum of the (C, α) matrix is determined, where the matrix is regarded as an operator on certain Banach sequence spaces. In particular the point spectrum is obtained in the spaces I_p(X), with 1<p≤∞, where X is a Banach space.