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Fresh Examples of Hyponormal Terraced Matrices with Transcendental Entries

Functional Analysis 2018-08-08 v1

Abstract

This note calls attention to an alternative version of the main result from [4], which can be used together with Maclaurin series expansions and trigonometric identities to show that the terraced matrices generated by the sequences {ln(1+1/(n+1)):n0}\{\ln (1+1/(n+1)) : n \geq 0\}, {tan(1/(n+2)):n0}\{\tan (1/(n+2)) : n \geq 0\}, and {sinh(1/(n+2)):n0}\{\sinh (1/(n+2)) : n \geq 0\} are hyponormal operators on 2\ell^2. Along the way it is also shown that the matrix generated by {tan(1/(n+1)):n0}\{\tan (1/(n+1)) : n \geq 0\} is not a hyponormal operator on 2\ell^2.

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Cite

@article{arxiv.1808.02300,
  title  = {Fresh Examples of Hyponormal Terraced Matrices with Transcendental Entries},
  author = {H. C. Rhaly},
  journal= {arXiv preprint arXiv:1808.02300},
  year   = {2018}
}

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6 pages