The notion of regularity for two dimensional matrix transformations was presented by Silverman [40] and Toeplitz [41].

Also, in [35]-[38], and [39] the four dimensional matrix transformation [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] was studied extensively by Robison and Hamilton.

Characterisations of classes of matrix transformations between sequence spaces constitute a wide, interesting and important field in both summability and operator theory.

The [beta]-duals play a much more important role than the continuous duals in the theory of sequence spaces and matrix transformations.

Matrix transformations of [lambda]-boundedness fields of normal matrix methods.

The matrix transformation y = Mx exists for each x 2 [m.

Specific topics include a survey of Kalton's work, twisted dualities in Banach space theory, complexity and homogeneity in Banach spaces, conditions for stochastic integrability in UMD Banach spaces, a new infinite game for Banach spaces with applications, greedy approximation in Banach spaces, Kolmogorov numbers of

matrix transformations, a general Baker super-stability criterion for the D'Alembert functional equation, aspects of probabilistic Littlewood-Paley theory, properties related to the Dauavet property, perturbations of ideal complements and asymptotically transitive Banach spaces.

Keywords: Time scales, function spaces, duals, matrix transformations.

In Section 4, we study infinite matrix transformations on special time scales as an application of the results in the earlier sections.

Matrix transformation involving [chi] were characterized by Sridhar [20] and Sirajiudeen [21].

Also, in [46] - [49] and [50] the four dimensional

matrix transformation [(Ax).

Turkmenoglu:

Matrix transformation between some classes of double sequences; Jour.