Abstract
“Property (UWE) holds” for an operator when the complement in the approximate point spectrum of the “essential approximate point spectrum” coincides with the isolated points of the spectrum which are eigenvalues. In this paper, we give the necessary and sufficient conditions for linear bounded operators and their functions for which property (UWE) holds. In addition, we explore how property (UWE) survives for 2×2 upper triangular operator matrices.
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