DIMENSIONS OF COMPLEX HILBERT SPACES ARE DETERMINED BY THE COMMUTATIVITY RELATION

作者：Kuzma Bojan^*

来源：Journal of Operator Theory, 2018, 79(1): 201-211.

DOI：10.7900/jot.2017feb13.2169

• Hilbert space
• Banach algebra
• commutativity
• commuting graph

Let H and K be complex Hilbert spaces. Assuming the set-theoretical axiom on generalized continuum hypothesis it is shown that if the commutativity relation in B(H), the algebra of bounded linear operators on H, is the same as in B(K), then dim H = dim K.

• 出版日期2018