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\(\mathbb{D}\)-topological duals of bicomplex \(\mathbb{BC}\)-modules \(l_p^{\Bbbk}(\mathbb{BC})\). (English) Zbl 1513.46007

Summary: In this paper, we present the concept of \(\mathbb{D}\)-topological dual of a \(\mathbb{BC}\)-module \(X\) with a \(\mathbb{D}\)-norm \(\Vert .\Vert_{\mathbb{D},X}\) and we find \(\mathbb{D}\)-topological duals of \(\mathbb{D}\)-normed bicomplex \(\mathbb{BC}\)-modules \(l_p^{\Bbbk}(\mathbb{BC})\) for \(1\leq p<\infty\). We also investigate some fundamental topological properties of bicomplex \(\mathbb{BC}\)-modules \(l_p^{\Bbbk}(\mathbb{BC})\) by defining some topological concepts such as solid space, monotone space, \(BK\)-space, symmetric space in the bicomplex setting by using the \(\mathbb{D}\)-norm \(\Vert .\Vert_{\Bbbk}\).

MSC:

46A45 Sequence spaces (including Köthe sequence spaces)
46B45 Banach sequence spaces
40A05 Convergence and divergence of series and sequences
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