컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0139 |
|---|---|
| 분류(Section) | Special Session |
| 분과(Session) | (SS-10) Function Theory, Operator Theory and Applications (SS-10) |
| 발표시간(Time) | 20th-C-10:00 -- 10:20 |
| 영문제목 (Title(Eng.)) |
Algebraic structure of certain subsets of Orlicz-Lorentz spaces |
| 저자(Author(s)) |
Hyung-Joon Tag1, Luis Bernal-González2, Daniel L. Rodríguez-Vidanes3, Juan B. Seoane-Sepúlveda3 Dongguk University1, Universidad de Sevilla2, Universidad Complutense de Madrid3 |
| 초록본문(Abstract) | The lineability problem concerns the existence of vector subspaces and other algebraic structures in sets that do not seem to form a vector subspace (e. g. Weierstrass monsters in $C[0,1]$). This notion has been explored not only in various Banach spaces such as $L_p$-spaces and the spaces of bounded linear operators but also in certain objects in dynamical systems, for instance, the set of universal vectors that exhibit a chaotic behavior under the action of a linear operator. In this talk, we focus on the lineability problem of certain nonlinear subsets of Orlicz-Lorentz spaces, which are known to be a natural generalization of both Orlicz and Lorentz spaces. We show that not only do these subsets contain infinite-dimensional vector subspaces, but also some of them exhibit topological genericity. We also identify certain subsets of Orlicz-Lorentz spaces where the lineability problem is not valid through characterizations of disjointly strictly singular inclusion operators between Orlicz-Lorentz spaces. This is joint work with Luis Bernal-González, Daniel L. Rodríguez-Vidanes, and Juan B. Seoane-Sepúlveda. |
| 분류기호 (MSC number(s)) |
46E30, 15A03, 46B87 |
| 키워드(Keyword(s)) | Lineability, spaceability, Orlicz-Lorentz space |
| 강연 형태 (Language of Session (Talk)) |
Korean |