Algebraic and triangular \(n\)-hyponormal operators. (English) Zbl 0877.47015

Ko, Eungil

Proc. Am. Math. Soc. 123, No. 11, 3473-3481 (1995).

Summary: We prove that if an operator \(T\in{\mathcal L}(\oplus_1^n{\mathbf H})\) is a finite triangular operator matrix with hyponormal operators on main diagonal, then \(T\) is subscalar. As corollaries we get the following:
(1) Every algebraic operator is subscalar.
(2) Every operator on a finite-dimensional complex space is subscalar.
(3) Every triangular \(n\)-hyponormal operator is subscalar.

MSC:

47B20	Subnormal operators, hyponormal operators, etc.
47B40	Spectral operators, decomposable operators, well-bounded operators, etc.
47B38	Linear operators on function spaces (general)

Keywords:

finite triangular operator matrix; hyponormal operators; subscalar