On double summability methods $\left| \mathcal{A}_{f}\right| _{k}$ and $\left| C,0,0\right|_{s}$

Left derivable or Jordan left derivable mappings on Banach algebras

‎Let $mathcal{A}$ be a unital Banach algebra‎, ‎$mathcal{M}$ be a left $mathcal{A}$-module‎, ‎and $W$ in $mathcal{Z}(mathcal{A})$ be a left separating point of $mathcal{M}$‎. ‎We show that if $mathcal{M}$ is a unital left $mathcal{A}$-module and $delta$ is a linear mapping from $mathcal{A}$ into $mathcal{M}$‎, ‎then the following four conditions are equivalent‎: ‎(i) $delta$ is a Jordan left de...

On Jordan left derivations and generalized Jordan left derivations of matrix rings

Abstract. Let R be a 2-torsion free ring with identity. In this paper, first we prove that any Jordan left derivation (hence, any left derivation) on the full matrix ringMn(R) (n 2) is identically zero, and any generalized left derivation on this ring is a right centralizer. Next, we show that if R is also a prime ring and n 1, then any Jordan left derivation on the ring Tn(R) of all n×n uppe...

On Summability of Double Series*

On double Hausdorff summability method

*Correspondence: [email protected] Department of Mathematics, İstanbul Commerce University, Sütlüce/Beyoğlu, İstanbul, Turkey Abstract Das (Proc. Camb. Philos. Soc. 67:321-326, 1970) proved that every conservative Hausdorff matrix is absolutely kth power conservative. Savaş and Rhoades (Anal. Math. 35:249-256, 2009) proved the result of Das for double Hausdorff summability. In this paper we...

Double - Inlet Left Ventricle

Two pathological specimens are presented in which the morphological left ventricle contains the right atrioventricular ostium, completely or in its major portion and, totally, the left atrioventricular ostium. It is suggested from a consideration of these cases and of the pathological material available in the literature that this constitutes an entity that can be usefully separated from the he...