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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
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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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |