Matrix Transformations of Starshaped Sequences

On the Spaces of $lambda _{r}$-almost Convergent and $lambda _{r}$-almost Bounded Sequences

The aim of the present work is to introduce the concept of $lambda _{r}$-almost convergence of sequences. We define the spaces $fleft( lambda _{r}right) $ and $f_{0}left( lambda _{r}right) $ of $ lambda _{r}$-almost convergent and $lambda _{r}$-almost null sequences. We investigate some inclusion relations concerning those spaces with examples and we determine the $beta $- and $gamma $-duals of...

On p-semilinear transformations

In this paper, we introduce $p$-semilinear transformations for linear algebras over a field ${bf F}$ of positive characteristic $p$, discuss initially the elementary properties of $p$-semilinear transformations, make use of it to give some characterizations of linear algebras over a field ${bf F}$ of positive characteristic $p$. Moreover, we find a one-to-one correspondence between $p$-semiline...

Some matrix transformations and generalized core of double sequences

A four-dimensional matrix transformation is said to be regular if it maps every bounded-convergent double sequence into a convergent sequence with the same limit. Firstly, Robison [G.M. Robison, Divergent double sequences and series, Trans. Amer. Math. Soc. 28 (1926) 50–73] presented the necessary and sufficient conditions for regular matrix transformations of double sequences. In this paper, t...

On One-Sided Ideals of Rings of Linear Transformations

Transformations computations‎: ‎Power‎, ‎Roots and Inverse

‎This paper presents some results of an annihilated element in Banach algebra‎, ‎and in specific case‎, ‎for any square matrix‎. The developed method significantly improves the computational aspects of transformations calculus and especially for finding powers and roots of any annihilated element‎. ‎An example is given to compare the proposed method with some other methods to show the efficienc...