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Journal of Operator Theory

Volume 79, Issue 1,  Winter 2018  pp. 201-211.

Dimensions of complex Hilbert spaces are determined by the commutativity relation

Authors:  Bojan Kuzma
Author institution:University of Primorska, Koper, SI-6000 Slovenia, \textit{and} IMFM, Jadranska 19, SI-1000 Ljubljana, Slovenia

Summary: Let H and K be complex Hilbert spaces. Assuming the set-theore\-tical axiom on generalized continuum hypothesis it is shown that if the commutativity relation in B(\HH), the algebra of bounded linear operators on H, is the same as in B(K), then dimH=dimK.

DOI: http://dx.doi.org/10.7900/jot.2017feb13.2169
Keywords: Hilbert space, Banach algebra, commutativity, commuting graph

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