Browder-type Theorems for Direct sums of Operators

ZARIOUH Hassan, ARROUD Abdelmajid


In this paper we study the stability of Browder-type Theorems for orthogonal direct sums.
Counterexamples show that in general properties (Bw); (Bb); (Baw) and (Bab) are not pre-
served under direct sums. Moreover, we characterize the stability of the property (Bb) under
direct sum via union of B-Weyl spectra of its summands. We also obtain analogous results for
properties (Baw); (Bab) and (Bw) with extra assumptions. The theory is exemplied in the
case of some special classes of operators.

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