Affiliation:
1. College of Computer and Information Technology, Henan Normal University, Xinxiang, China
2. College of Mathematics and Information Science, Henan Normal University, Xinxiang, China
3. School of Mathematical Science, Inner Mongolia Normal University, Hohhot, China
Abstract
For some operator A ? B(H), positive integers m and k, an operator T ? B(H)
is called k-quasi-(A,m)-symmetric if T*k( mP j=0 (?1)j(m j )T*m?jATj)Tk =
0, which is a generalization of the m-symmetric operator. In this paper,
some basic structural properties of k-quasi-(A,m)-symmetric operators are
established with the help of operator matrix representation. We also show
that if T and Q are commuting operators, T is k-quasi-(A,m)-symmetric and Q
is n-nilpotent, then T + Q is (k + n ? 1)-quasi-(A,m + 2n ? 2)-symmetric. In
addition, we obtain that every power of k-quasi-(A,m)-symmetric is also
k-quasi-(A,m)-symmetric. Finally, some spectral properties of
k-quasi-(A,m)-symmetric are investigated.
Publisher
National Library of Serbia
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