Gowda, Huche; Lokesha, V. Generalised orthogonal projections on Banach spaces. (English) Zbl 1243.46012 Acta Cienc. Indica, Math. 24, No. 3, 271-274 (1998). Summary: Let \(X\) be a complex Banach space and \(\mathbf{B}(\mathbf{X})\) the space of all bounded linear operators on \(\mathbf{X}\). An operator \(\mathbf{X} \in \mathbf{B}(\mathbf{X})\) is said to be a generalized orthogonal projection on \(\mathbf{X}\) if it is a projection and if there is support mapping \(\phi : \mathbf{X} \to \mathbf{X}^{\ast}\) such that \(\phi \mathbf{X} = \mathbf{X}^{\ast} \phi\). In this paper, we prove some results on generalized orthogonal projections on \(\mathbf{X}\). MSC: 46C50 Generalizations of inner products (semi-inner products, partial inner products, etc.) 46B99 Normed linear spaces and Banach spaces; Banach lattices Keywords:semi-inner product; generalised orthogonal projections; strict convexity PDFBibTeX XMLCite \textit{H. Gowda} and \textit{V. Lokesha}, Acta Cienc. Indica, Math. 24, No. 3, 271--274 (1998; Zbl 1243.46012)