Various notion of equality of spectra and essential spectra of quasi similar operators have been studied, but the same results has not been reflected clearly with ω(A) . This paper shows that the theory for the notion of ω(A) simplifies if the underlying space is a separable infinite dimensional Hilbert space and the operator is reduced by its finite-dimensional eigenvalues. As an application this paper investigate ω(A) and quasi-similar bi-quasi-triangular operator.
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