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Matrix transformations of summability domains of generalized matrix methods in Banach spaces

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Abstract

The necessary and sufficient conditions for a matrix M to be a transform from the summability domain of generalized matrix method A into the summability domain of another generalized matrix method B are proved. The elements of Mare continuous linear operators from a Banach space X into another Banach space Y, and the elements of A and B are continuous linear operators from X into X and from Y into Y, respectively. As a special case there are considered the case when A is the generalized Riesz method.

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Correspondence to Ants Aasma.

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Aasma, A. Matrix transformations of summability domains of generalized matrix methods in Banach spaces. Rend. Circ. Mat. Palermo 58, 467–476 (2009). https://doi.org/10.1007/s12215-009-0036-9

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  • DOI: https://doi.org/10.1007/s12215-009-0036-9

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