Ideal spaces of measurable operators affiliated to a semifinite von Neumann algebra. II (Q6551246)

This is a continuation of [\textit{A. M. Bikchentaev}, Sib. Math. J. 59, No. 2, 243--251 (2018; Zbl 06908372); translation from Sib. Mat. Zh. 59, No. 2, 309--320 (2018)]. In the present paper, the authors establish several results in the setting of normed ideal spaces of \(\tau\)-measurable operators affiliated with a semifinite von Neumann algebra which extend results in the literature for noncommutative symmetric spaces. One of the main results of this paper is the following: \N\[\N\left\|A\right\|_\mathcal{E}\le \left\| A+i B\right\|_\mathcal{E}\N\]\Nfor any self-adjoint operators \(A\) and \(B\) in a normed ideal space \(\mathcal{E}\) affiliated with a semifinite von Neumann algebra \(\mathcal{M}\).