Weylness of 2 × 2 operator matrices

Xiufeng Wu, Junjie Huang and Alatancang Chen

Mathematische Nachrichten, 2018, vol. 291, issue 1, 187-203

Abstract: Let H and K be complex separable infinite†dimensional Hilbert spaces. Given the operators A∈B(H),B∈B(K) and C∈B(K,H), we define MX:=[ACXB] where X∈B(H,K) is an unknown element. In this paper, a necessary and sufficient condition is given for MX to be a right Weyl (left Weyl, or Weyl) operator for some X∈B(H,K). Moreover, some relevant properties and illustrating examples are also given.

Date: 2018
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