Almost commuting matrices need not be nearly commuting

Author:
Man Duen Choi

Journal:
Proc. Amer. Math. Soc. **102** (1988), 529-533

MSC:
Primary 47A55; Secondary 15A27, 47B47

DOI:
https://doi.org/10.1090/S0002-9939-1988-0928973-3

MathSciNet review:
928973

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the collection of complex matrices with the Hilbert-space-operator norm. There exist two concrete matrices with , but for all commuting pairs . It is shown explicitly that there is a natural obstruction which prevents almost commuting matrices to get close to any commuting pairs.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1988-0928973-3

Keywords:
Almost commuting matrices,
Hilbert-space-operator norm,
signature of a matrix,
commuting approximant,
pertubation

Article copyright:
© Copyright 1988
American Mathematical Society