Ordered Structures of Constructing Operators for Generalized Riesz Systems
A sequence {φn} in a Hilbert space H with inner product <·,·> is called a generalized Riesz system if there exist an ONB e={en} in H and a densely defined closed operator T in H with densely defined inverse such that {en}⊂D(T)∩D((T-1)⁎) and Ten=φn, n=0,1,⋯, and (e,T) is called a constructing p...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2018-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2018/3268251 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832561945294667776 |
|---|---|
| author | Hiroshi Inoue |
| author_facet | Hiroshi Inoue |
| author_sort | Hiroshi Inoue |
| collection | DOAJ |
| description | A sequence {φn} in a Hilbert space H with inner product <·,·> is called a generalized Riesz system if there exist an ONB e={en} in H and a densely defined closed operator T in H with densely defined inverse such that {en}⊂D(T)∩D((T-1)⁎) and Ten=φn, n=0,1,⋯, and (e,T) is called a constructing pair for {φn} and T is called a constructing operator for {φn}. The main purpose of this paper is to investigate under what conditions the ordered set Cφ of all constructing operators for a generalized Riesz system {φn} has maximal elements, minimal elements, the largest element, and the smallest element in order to find constructing operators fitting to each of the physical applications. |
| format | Article |
| id | doaj-art-eb16c10a9e7f44d5abd1f61aa8f3aff4 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-eb16c10a9e7f44d5abd1f61aa8f3aff42025-02-03T01:23:58ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252018-01-01201810.1155/2018/32682513268251Ordered Structures of Constructing Operators for Generalized Riesz SystemsHiroshi Inoue0Center for Advancing Pharmaceutical Education, Daiichi University of Pharmacy, 22-1 Tamagawa-cho, Minami-ku, Fukuoka 815-8511, JapanA sequence {φn} in a Hilbert space H with inner product <·,·> is called a generalized Riesz system if there exist an ONB e={en} in H and a densely defined closed operator T in H with densely defined inverse such that {en}⊂D(T)∩D((T-1)⁎) and Ten=φn, n=0,1,⋯, and (e,T) is called a constructing pair for {φn} and T is called a constructing operator for {φn}. The main purpose of this paper is to investigate under what conditions the ordered set Cφ of all constructing operators for a generalized Riesz system {φn} has maximal elements, minimal elements, the largest element, and the smallest element in order to find constructing operators fitting to each of the physical applications.http://dx.doi.org/10.1155/2018/3268251 |
| spellingShingle | Hiroshi Inoue Ordered Structures of Constructing Operators for Generalized Riesz Systems International Journal of Mathematics and Mathematical Sciences |
| title | Ordered Structures of Constructing Operators for Generalized Riesz Systems |
| title_full | Ordered Structures of Constructing Operators for Generalized Riesz Systems |
| title_fullStr | Ordered Structures of Constructing Operators for Generalized Riesz Systems |
| title_full_unstemmed | Ordered Structures of Constructing Operators for Generalized Riesz Systems |
| title_short | Ordered Structures of Constructing Operators for Generalized Riesz Systems |
| title_sort | ordered structures of constructing operators for generalized riesz systems |
| url | http://dx.doi.org/10.1155/2018/3268251 |
| work_keys_str_mv | AT hiroshiinoue orderedstructuresofconstructingoperatorsforgeneralizedrieszsystems |