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Spectral theory of ordered pairs of the linear operators - acting in different Banach spaces and applications

2007
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International Mathematical Forum
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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 pair

doi:10.12988/imf.2007.07021
fatcat:b5scl4zhkbauvgyxtyjiicagia