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Some new sequence spaces which include the spaces p and . (English) Zbl 1096.46005
Summary: We introduce the sequence space a p r of non-absolute type and prove that the spaces a p r and p are linearly isomorphic for 0<p. We also show that a p r , which includes the space p , is a p-normed space and a BK space in the cases of 0<p<1 and 1p, respectively. Furthermore, we give some inclusion relations and determine the α-, β- and γ-duals of the space a p r and construct its basis. We devote the last section of the paper to the characterization of the matrix mappings from the space a p r to some of the known sequence spaces and to some new sequence spaces.
MSC:
46A45Sequence spaces
46B45Banach sequence spaces
46A35Summability and bases in topological linear spaces