2024/02/02 by Alexander Pushnitski, Pushnitski, Alexander, František Štampach +1
Computer Science · Mathematics · #Matrix Theory and Algorithms #Holomorphic and Operator Theory #Approximation Theory and Sequence Spaces
paper · pdf · doi:10.48550/arxiv.2402.01237
We consider the class of bounded symmetric anti-linear operators B with a cyclic vector. We associate with B the spectral data consisting of a probability measure and a function. In terms of the spectral data of B, we introduce a functional model operator B acting on a model space. We prove an anti-linear variant of the spectral theorem demonstrating that B is unitarily equivalent to B. Next, we show that B is also unitarily equivalent to an anti-linear tridiagonal operator and discuss connection with orthogonal polynomials in the anti-linear setting.