ACTA issues

Weyl's theorems: continuity of the spectrum and quasihyponormal operators

Slaviša V. Djordjević, Dragan S. Djordjević

Acta Sci. Math. (Szeged) 64:1-2(1998), 259-269

Abstract. We consider various Weyl's theorems in connection with the continuity of the reduced minimum modulus, Weyl spectrum, Browder spectrum, essential approximate point spectrum and Browder essential approximate point spectrum. If $H$ is a Hilbert space, and $T\in B(H)$ is a quasihyponormal operator, we prove the spectral mapping theorem for the essential approximate point spectrum and for arbitrary analytic function, defined on some neighbourhood of $\sigma(T)$. Also, if $T^*$ is quasihyponormal, we prove that the $a$-Weyl's theorem holds for $T$.

AMS Subject Classification (1991): 47A53, 47B20

Keyword(s): Semi--Fredholm operators, essential spectra, Weyl's theorems, spectral continuity, quasihyponormal operators

Received August 15, 1996 and in revised form October 29, 1997. (Registered under 2661/2009.)