ACTA issues

The strong irreducibility of hyponormal operators and Berezin perturbation

Chun Lan Jiang, Kuen Yu Guo

Acta Sci. Math. (Szeged) 64:1-2(1998), 231-248

Abstract. It is shown that given a co-hyponormal and quasitriangular operator $T$ with connected spectrum, there exists a compact $K$ such that $T+K$ is strongly irreducible. Using the above result, we prove that every analytic {\it Toeplitz operator} on Bergman space $L_a^2({\cal B}_{n}, dv)$ is the sum of a strongly irreducible Toeplitz operator and a Berezin perturbation, where ${\cal B}_{n}$ is the unite ball of complex n-dimensional space and $n\geq1$.

AMS Subject Classification (1991): 47A10, 47A55, 47A58

Keyword(s): hyponormal operaters, Berezin perturbation, Strongly irreducible operator

Received July 7, 1997 and in revised form November 14, 1997. (Registered under 2659/2009.)