Cesàro sums and algebra homomorphisms of bounded operators

Let g:= gl_m|_n be a general linear Lie superalgebra over an algebraically closed field k:= \({\bar F_p}\) of characteristic p > 2. A module of g is said to be of Kac–Weisfeiler type if its dimension coincides with the dimensional lower bound in the super Kac–Weisfeiler property presented by Wang–Zhao in [9]. In this paper, we verify the existence of the Kac–Weisfeiler modules for gl_m|_n. We also establish the corresponding consequence for the special linear Lie superalgebra sl_m|_n with the restrictions that p > 2 and p ? (m - n).     

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...     

Spectral Properties of Generalized Cesàro Operators

We investigate spectral properties of operators on H² of the form

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.     

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.     

A note on the powers of Cesàro bounded operators

In this note we give a negative answer to Zemánek’s question (1994) of whether it always holds that a Cesàro bounded operator T on a Hilbert space with a single spectrum satisfies $ \mathop {\lim }\limits_{n \to \infty } $ \mathop {\lim }\limits_{n \to \infty } ∥T ⁿ⁺¹ − T ⁿ ∥ = 0.     

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

We investigate spectral properties of integral operators of the form

Cesàro-type operators on Hardy, BMOA and bloch spaces

Let H ^p, p ∈ (0, ∞], BMOA and B ^a, a ∈ (0, ∞) be the classical p-Hardy, analytic BMO(∂) (bounded mean oscillation on the unit circle) and a-Bloch space on the unit disk. In this paper, we prove that the Cesàro-type operator: C ^α, α ∈ (−1, ∞) is bounded on H ^p, p ∈ (0, ∞) and on B ^a, a ∈ (1, ∞), but, unbounded on H ^∞, BMOA and B ^a, a ∈ (0, 1]. In particular, we give an answer to the Stempak’s open problem.     

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.     

Cesàro summability of one- and two-dimensional Walsh-Fourier series

ВВОДьтсьp-кВАжИлОкАл ьНыЕ ОпЕРАтОРы И ОДНО МЕРНыЕ ДИАДИЧЕскИЕ МАРтИНг АльНыЕ пРОстРАНстВА хАРДИH _p . ДОкАжАНО, ЧтО ЕслИ сУБлИНЕИНыИ ОпЕРАтО РT p-кВАжИлОкАлЕН И ОгРА НИЧЕН ИжL _∞ ВL _∞, тО ОН ьВльЕтсь тАкжЕ ОгРАН ИЧЕННыМ ИжH _p ВL _p , (0<p<1). В кАЧЕстВЕ пРИ лОжЕНИь ДОкАжАНО, ЧтО МАксИМАльНыИ ОпЕРАт ОР ОДНОгО ЧЕжАРОВскОгО пАРАМЕтРА И МОДИФИцИ РОВАННых ЧЕжАРОВскИх сРЕДНИх МАРтИНгАлА ьВльЕтсь ОгРАНИЧЕННыМ ИжH _p ВL _p И ИМЕЕт слАБыИ тИп (L ₁,L ₁). Мы ВВОДИМ ДВУМЕРНыИ ДИА ДИЧЕскИИ гИБРИД пРОс тРАНстВ хАРДИH ₁ И пОкАжыВАЕМ, Ч тО МАксИМАльНыИ ОпЕРАт ОР сРЕДНИх ЧЕжАРО ДВУ МЕРНОИ ФУНкцИИ ИМЕЕт слАБыИ тИп (H ₁ ^# ,L ₁). тАк Мы пОлУЧАЕМ, Ч тО ДВУпАРАМЕтРИЧЕск ИЕ сРЕДНИЕ ЧЕжАРО ФУНкц ИИf ?H ₁ ^# ?L logL схОДьтсь пОЧтИ ВсУДУ к ИсхОДНОИ ФУНк цИИ.     

Estimate of the approximation of periodic functions by negative Cesàro means

The problem of approximation of continuous functions by Cesàro (C,α)-means, −1 < α < 0, in terms of L _p and C-modulus of continuity is studied.     

Cesàro Summation for Random Fields

Various methods of summation for divergent series of real numbers have been generalized to analogous results for sums of i.i.d. random variables. The natural extension of results corresponding to Cesàro summation amounts to proving almost sure convergence of the Cesàro means. In the present paper we extend such results as well as weak laws and results on complete convergence to random fields, more specifically to random variables indexed by ℤ₊², the positive two-dimensional integer lattice points.     

On Subspaces of Cesàro Spaces

We obtain a characterization of subspaces of L _p , with 1 < p < ∞, on which the L _p -norm is equivalent to the norm of the Cesàro space Ces _p . Also, we show that Ces _p has a complemented copy of the Cesàro sequence space ces _p .     

Embeddings between weighted Copson and Cesàro function spaces

In this paper, characterizations of the embeddings between weighted Copson function spaces \(Co{p_{{p_1},{q_1}}}\left( {{u_1},{v_1}} \right)\) and weighted Cesàro function spaces \(Ce{s_{{p_2},{q_2}}}\left( {{u_2},{v_2}} \right)\) are given. In particular, two-sided estimates of the optimal constant c in the inequality

$${\left( {\int_0^\infty {{{\left( {\int_0^t {f{{\left( \tau \right)}^{{p_2}}}{v_2}\left( \tau \right)d\tau } } \right)}^{{q_2}/{p_2}}}{u_2}\left( t \right)dt} } \right)^{1/{q_2}}} \leqslant c{\left( {\int_0^\infty {{{\left( {\int_t^\infty {f{{\left( \tau \right)}^{{p_1}}}{v_1}\left( \tau \right)d\tau } } \right)}^{{q_1}/{p_1}}}{u_1}\left( t \right)dt} } \right)^{1/{q_1}}},$$

where p₁, p₂, q₁, q₂ ∈ (0,∞), p₂ ≤ q₂ and u₁, u₂, v₁, v₂ are weights on (0,∞), are obtained. The most innovative part consists of the fact that possibly different parameters p₁ and p₂ and possibly different inner weights v₁ and v₂ are allowed. The proof is based on the combination of duality techniques with estimates of optimal constants of the embeddings between weighted Cesàro and Copson spaces and weighted Lebesgue spaces, which reduce the problem to the solutions of iterated Hardy-type inequalities.

     

Bloch-type spaces and extended Cesàro operators in the unit ball of a complex Banach space

Let B be the unit ball of a complex Banach space X. In this paper, we generalize the Bloch-type spaces and the little Bloch-type spaces to the open unit ball B by using the radial derivative. Next, we de?ne an extended Ces`aro operator T_φ with the holomorphic symbol φ and characterize those φ for which T_φ is bounded between the Bloch-type spaces and the little Bloch-type spaces. We also characterize those φ for which T_φ is compact between the Bloch-type spaces and the little Bloch-type spaces under some additional assumption on the symbol φ. When B is the open unit ball of a ?nite dimensional complex Banach space X, this additional assumption is automatically satis?ed.