Abstract
We investigate the effect of four‐dimensional matrix transformation on new classes of double sequences. Stretchings of a double sequence is defined, and this definition is used to present a four‐dimensional analogue of D. Dawson′s copy theorem for stretching of a double sequence. In addition, the multidimensional analogue of D. Dawson′s copy theorem is used to characterize convergent double sequences using stretchings.
Highlights
In this paper, RH-regular matrices and the stretching of double sequences are used to characterize P -convergent sequences
To achieve this goal we begin by defining an -Pringsheim-copy and a stretching of double sequences
The copy theorem of Dawson in [1] will be extended as follows: if each of A and T is an RH-regular matrix, and x is any bounded double complex sequence with being any bounded positive term double sequence with P -limi,j i,j = 0, there exists a stretching y of x such that T (Ay) exists and contains an -Pringsheim-copy of x
Summary
RH-regular matrices and the stretching of double sequences are used to characterize P -convergent sequences. As another example of a subsequence of a double sequence, we define x as follows: Note that if the double sequence x contains at most a finite number of unbounded rows and/or columns, every subsequence of x is bounded.
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