Crystal complex symmetric operators

Eungil Ko, Ji Eun Lee, Mee Jung Lee

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


In this paper, we study properties of weak crystal operators. In particular, we show that if T∈ L(H) is a complex symmetric operator, then T is weak crystal, crystal, or crystal-like if and only if T is weak crystal, crystal, or crystal-like, respectively. Moreover, we prove that if T is a quasiaffinity, then T is weak crystal if and only if the Aluthge transform T~ (or the Duggal transform T~ D) of T is weak crystal. Finally, we give several applications of these results.

Original languageEnglish
Pages (from-to)1711-1727
Number of pages17
JournalBanach Journal of Mathematical Analysis
Issue number4
StatePublished - 1 Sep 2020

Bibliographical note

Publisher Copyright:
© 2020, Tusi Mathematical Research Group (TMRG).


  • Aluthge transform
  • Complex symmetric operator
  • Crystal operator
  • Crystal-like operator
  • Invariant subspace
  • Weak crystal operator


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