Crystal complex symmetric operators

Eungil Ko, Ji Eun Lee, Mee Jung Lee

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

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
Volume14
Issue number4
DOIs
StatePublished - 1 Sep 2020

Bibliographical note

Funding Information:
Eungil Ko was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT)(2019R1F1A1058633). Ji Eun Lee was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2019R1A2C1002653). Eungil Ko and Mee-Jung Lee were supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2019R1A6A1A11051177).

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

Keywords

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

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