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Some structural properties of Hausdorff matrices

1959
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Bulletin of the American Mathematical Society
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Definitions. Let A ~{a n k) denote an infinite matrix. A is called conservative if A has finite norm, ak = limn-«> cbnk exists for each fe, and lim«^oo ^kdnk exists. A is called multiplicative if A is conservative and ajfc = 0 for each k. s denotes the space of sequences, m the subspace of bounded sequences, and c the subspace of convergent sequences. E\ is the field of complex numbers and £«> the set of sequences, each of which possesses only a finite number of nonzero terms. Let x be a fixed

doi:10.1090/s0002-9904-1959-10256-1
fatcat:ptpzt7clcjdfnlgjh4pnjzmnke