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

M. Sahin, M. B. Ragimov
2007 International Mathematical Forum  
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
more » ... , B), which allow to apply theory of commutative Banach algebras and spectral theory of the operators, acting in one space. In sections (1,2) we give the number of general results on the spectrum of operators pairs (A, B) in dependence on some properties of the operator B (connected with invertibility, finite dimensionless and etc.).
doi:10.12988/imf.2007.07021 fatcat:b5scl4zhkbauvgyxtyjiicagia