On Properties of Class A(n) and n-Paranormal Operators
Let n be a positive integer, and an operator T∈B(ℋ) is called a class A(n) operator if T1+n2/1+n≥|T|2 and n-paranormal operator if T1+nx1/1+n≥||Tx|| for every unit vector x∈ℋ, which are common generalizations of class A and paranormal, respectively. In this paper, firstly we consider the tensor pro...
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| Format: | Article |
| Language: | English |
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2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/629061 |
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| author | Xiaochun Li Fugen Gao |
| author_facet | Xiaochun Li Fugen Gao |
| author_sort | Xiaochun Li |
| collection | DOAJ |
| description | Let n be a positive integer, and an operator T∈B(ℋ) is called a class A(n) operator if T1+n2/1+n≥|T|2 and n-paranormal operator if T1+nx1/1+n≥||Tx|| for every unit vector x∈ℋ, which are common generalizations of class A and paranormal, respectively. In this paper, firstly we consider the tensor products for class A(n) operators, giving a necessary and sufficient condition for T⊗S to be a class A(n) operator when T and S are
both non-zero operators; secondly we consider the properties for n-paranormal operators, showing that a n-paranormal contraction is the direct sum of a unitary and a C.0 completely non-unitary contraction. |
| format | Article |
| id | doaj-art-c1d70660b32a415a86c57ae1256c6f36 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-c1d70660b32a415a86c57ae1256c6f362025-02-03T05:51:48ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/629061629061On Properties of Class A(n) and n-Paranormal OperatorsXiaochun Li0Fugen Gao1College of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan 453007, ChinaCollege of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan 453007, ChinaLet n be a positive integer, and an operator T∈B(ℋ) is called a class A(n) operator if T1+n2/1+n≥|T|2 and n-paranormal operator if T1+nx1/1+n≥||Tx|| for every unit vector x∈ℋ, which are common generalizations of class A and paranormal, respectively. In this paper, firstly we consider the tensor products for class A(n) operators, giving a necessary and sufficient condition for T⊗S to be a class A(n) operator when T and S are both non-zero operators; secondly we consider the properties for n-paranormal operators, showing that a n-paranormal contraction is the direct sum of a unitary and a C.0 completely non-unitary contraction.http://dx.doi.org/10.1155/2014/629061 |
| spellingShingle | Xiaochun Li Fugen Gao On Properties of Class A(n) and n-Paranormal Operators Abstract and Applied Analysis |
| title | On Properties of Class A(n) and n-Paranormal Operators |
| title_full | On Properties of Class A(n) and n-Paranormal Operators |
| title_fullStr | On Properties of Class A(n) and n-Paranormal Operators |
| title_full_unstemmed | On Properties of Class A(n) and n-Paranormal Operators |
| title_short | On Properties of Class A(n) and n-Paranormal Operators |
| title_sort | on properties of class a n and n paranormal operators |
| url | http://dx.doi.org/10.1155/2014/629061 |
| work_keys_str_mv | AT xiaochunli onpropertiesofclassanandnparanormaloperators AT fugengao onpropertiesofclassanandnparanormaloperators |