On the existence of uniformly bounded self-adjoint bases in GNS spaces

Debabrata De; Kunal Mukherjee

doi:10.4171/dm/941

JournalsdmVol. 28, No. 6pp. 1381–1392

On the existence of uniformly bounded self-adjoint bases in GNS spaces

Debabrata De
National Institute of Science Education and Research, Khurda, India
Kunal Mukherjee
Indian Institute of Technology Madras, Tamil Nadu, India
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Abstract

The Gelfand–Naimark–Segal (GNS) space of a diffuse finite von Neumann algebra with respect to a faithful normal tracial state admits an orthonormal basis consisting of the image inside the GNS space of a uniformly bounded sequence of self-adjoint operators.

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Debabrata De, Kunal Mukherjee, On the existence of uniformly bounded self-adjoint bases in GNS spaces. Doc. Math. 28 (2023), no. 6, pp. 1381–1392

DOI 10.4171/DM/941