실적년도 | 2015 |
---|---|
논문구분 | 국외 |
총저자 | Piotr Budzyński, Zenon Jan Jabłoński, Il BongJung, Jan Stochel |
학술지명 | Journal of Mathematical Analysis and Applications |
권(Vol.) | 435 |
호(No.) | 1(302-314) |
게재년월 | 2016년 1월 |
Impact Factor | |
SCI 등재 | Y |
비고 |
In 1940 Naimark gave a remarkable example of a closed symmetric operator whose square has trivial domain (see [19]). In 1983 Chernoff published a short example of a semibounded closed symmetric operator whose square has trivial domain (see [11]). In the same year Schmüdgen found out another pathological behaviour of domains of powers of closed symmetric operators related to density with respect to graph norms (see [21]). It turns out that Naimark’s phenomenon can never happen in some concrete classes of operators. Among them are the class COof composition operators in L2-spaces and the class WSof weighted shifts on directed trees. The reason for this is that symmetric operators in these classes are automatically bounded (see [17,8]).