Abstract The classes of bounded operators on Banach spaces which satisfy a-Weyl’s theorem, Weyl’s theorem and the property (w) were studied by many authors. In this paper, we introduce and study the above three Weyl’s type theorems in the general context of multivalued linear operators. We begin by giving a variety of characterizations of the SVEP at a point of Kato finite type linear relations. Such characterizations will be the key to investigate the classes of linear relations which satisfy a-Weyl’s theorem, Weyl’s theorem and the property (w). As an application of the obtained results we present an example of linear relation which obeys a-Weyl’s theorem, Weyl’s theorem and it also has the property (w). We also give an example of linear relation such that the property (w), a-Weyl’s theorem and Weyl’s theorem fail for it.
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