Complex symmetric operators and isotropic vectors in Banach spaces via linear functionals (Research on structure of operators by order and related topics)

Abstract

We generalize the concept of complex symmetric operators 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. All this work is based on [M. Cho, I. Hur and J.E. Lee, Complex symmetric operators and isotropic vectors on Banach spaces, J. Math. Anal. Appl. 479 (2019), no. 1, 752-764.].