On Fong-Tsui conjecture and binormality of operators
Abstract In [Fong, C. K.—Tsui, S. K.: A note on positive operators , J. Operator Theory 5 (1) (1981), 73–76], the authors conjectured that T ∈ 𝔅( ℋ ) is self-adjoint if |T| ≤ |Re T |. After more than 40 years, the validity of the conjecture is still unknown. In this paper, we demonstrate, amongst other results, that the conjecture is true for binormal operators which are either injective, 2-quasinormal, or Im T is compact.
Authors
- Hranislav Stanković (ORCID: https://orcid.org/0000-0002-3418-9177)
Institutions
- University of Nis (RS)
Publication Details
- Journal
- Mathematica Slovaca
- Published
- 2025-10-01
- DOI
- https://doi.org/10.1515/ms-2025-0088
- Primary Topic
- Holomorphic and Operator Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00