In this paper, we analyze local spectral properties of operators R, S and RS which satisfy the operator equations RnSRn = Rj and Sn RSn = Sj for same integers j ≥ n ≥ 0. We also continue to study the relationship between the local spectral properties of an operator R and the local spectral properties of S. Thus, we investigate the transmission of some local spectral properties from R to S and we illustrate our results with an example. The theory is exemplified in some cases.
Triolo S. (2020). Local spectral theory for r and s satisfying rnsrn = rj. AXIOMS, 9(4), 1-8 [10.3390/axioms9040120].
Local spectral theory for r and s satisfying rnsrn = rj
Triolo S.
2020-10-01
Abstract
In this paper, we analyze local spectral properties of operators R, S and RS which satisfy the operator equations RnSRn = Rj and Sn RSn = Sj for same integers j ≥ n ≥ 0. We also continue to study the relationship between the local spectral properties of an operator R and the local spectral properties of S. Thus, we investigate the transmission of some local spectral properties from R to S and we illustrate our results with an example. The theory is exemplified in some cases.
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