Complex symmetric operators and isotropic vectors on Banach spaces
2019
Abstract In this paper, we generalize the concepts of isotropic vectors and complex symmetric operators from Hilbert spaces to Banach spaces via their dual spaces. With this extension we show the existence of isotropic vectors on Banach spaces whose dimension is at least two and the relation between the simplicity of an eigenvalue and the non-existence of its isotropic eigenvectors.
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