컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0113 |
|---|---|
| 분류(Section) | Special Session |
| 분과(Session) | (SS-10) Function Theory, Operator Theory and Applications (SS-10) |
| 발표시간(Time) | 20th-C-11:10 -- 11:30 |
| 영문제목 (Title(Eng.)) |
Linearity and lineability in sets of norm-attaining Lipschitz functions and their complements |
| 저자(Author(s)) |
Oscar Roldan Blay1 Dongguk University1 |
| 초록본문(Abstract) | Let M be a pointed metric, with a distinguished point 0. Denote Lip$_0$(M) the Banach space of Lipschitz functions on M that vanish at 0, and SNA(M) the subset of all such functions that strongly attain their norm (that is, they attain their biggest possible slope at some pair of points). In this talk we will discuss the linearity and the lineability of SNA(M) and its complement. In particular, we will show that these sets are never linear spaces, but they always contain infinite-dimensional Banach spaces. Several other related questions will also be discussed. This talk is based in a recent joint work with Geunsu Choi, Mingu Jung, and Han Ju Lee. The speaker is supported by Korean project NRF-2020R1A2C1A01010377 and Spanish project PID2021-122126NB-C33/MCIN/AEI/10.13039/501100011033 (FEDER). |
| 분류기호 (MSC number(s)) |
46B04, 46B87, 46B20, 54E50 |
| 키워드(Keyword(s)) | Linearity, lineability, spaceability, Lipschitz function, strongly norm-attaining |
| 강연 형태 (Language of Session (Talk)) |
English |