Characterisations of orthogonality in certain Banach spaces. (English) Zbl 1006.46022
Summary: We adopt the notion of orthogonality introduced by the author in a previous article. We establish a characterization for orthogonality in the spaces \(\ell^p_S(\mathbb{C})\), \(1\leq p<\infty\), where \(S\) is a set of positive integers and \(\mathbb{C}\) is the field of complex numbers. Generalizations of the usual characterization of orthogonality in the Hilbert spaces \(\ell^2_S(\mathbb{C})\), via inner products, are obtained.
MSC:
| 46C50 | Generalizations of inner products (semi-inner products, partial inner products, etc.) |
| 46B20 | Geometry and structure of normed linear spaces |
| 46B45 | Banach sequence spaces |
References:
| [1] | Singer, Acad. R. P. Romîne. Bul. Şti. Secţ. Şti. Mat. Fiz. 9 pp 29– (1957) |
| [2] | Roberts, Tôhoku Math. J. 39 pp 42– (1934) |
| [3] | DOI: 10.1215/S0012-7094-35-00115-6 · Zbl 0012.30604 · doi:10.1215/S0012-7094-35-00115-6 |
| [4] | DOI: 10.1215/S0012-7094-45-01223-3 · Zbl 0060.26202 · doi:10.1215/S0012-7094-45-01223-3 |
| [5] | Khalil, Math. J. Toyama Univ. 13 pp 185– (1990) |
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