Similarity and Unitary Equivalence

Mohammed Hichem Mortad
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Mohammed Hichem Mortad: University of Oran 1

Chapter Chapter 15 in Counterexamples in Operator Theory, 2022, pp 263-279 from Springer

Abstract: Abstract Clearly, A and B have the same eigenvalues which, in this setting, means that A and B have equal spectra. To see why A and B are not unitarily equivalent, remember that two unitarily equivalent operators are simultaneously (e.g.) self-adjoint. Since A is self-adjoint and B is not, it follows that they cannot be unitarily equivalent.

Date: 2022
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DOI: 10.1007/978-3-030-97814-3_15

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