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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