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Ordered pairs of linear operators (A, B) from Banach space L (X; Y ) of the linear bounded operators, defined on complex Banach space X with the values in complex Banach space Y are considered in this paper. Notion of singular set (spectrum) of the ordered pair (A, B) is introduced essentially with the help of operators bundle of the form and functional calculus in sections (1,2). For investigation of spectral properties of the pairs (A, B) we apply left and right pseudoresolvents of the pairdoi:10.12988/imf.2007.07021 fatcat:b5scl4zhkbauvgyxtyjiicagia