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 $\mathcal H$ and $\mathcal K$ be complex Hilbert spaces.
Assuming the set-theore\-tical axiom on generalized continuum
hypothesis it is shown that if the commutativity relation in $\mathscr B(\HH)$,
the algebra of bounded linear
operators on $\mathcal H $, is the same as in $\mathscr B(\mathcal K )$,
then $\dim\mathcal H =\dim\mathcal K $.
DOI: http://dx.doi.org/10.7900/jot.2017feb13.2169
Keywords: Hilbert space, Banach algebra, commutativity, commuting graph
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