On Bi-J-Class Bilinear Mappings on Banach Spaces
We propose the notion of J-set for a bilinear mapping to define the concept of bi-J-class bilinear mapping. We prove that every bihypercyclic bilinear mapping is bi-J-class, although its reverse does not necessarily hold. It is indicated that some properties of bi-J-class bilinear mappings are similar to J-class operators, but some relevant counterexamples are presented to show that many familiar properties of J-class operators are not valid for this framework. Next, we deal with the Kato’s approximation of bilinear mappings and discuss their bi-J-class properties.
KeywordsBihypercyclic bilinear mapping Bi-J-class bilinear mapping Approximation in the sense of Kato
Mathematics Subject Classification47A16 46G25 47B37
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