Some results on higher order symmetric operators
Filomat, Tome 37 (2023) no. 12, p. 3769
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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 (m j=0 (−1) j (m j)T * m−j AT j)T k = 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.
Classification :
47B20, 47A10
Keywords: (A, m)-symmetric operator, m-symmetric operator, Perturbation by nilpotent operator, Spectrum
Keywords: (A, m)-symmetric operator, m-symmetric operator, Perturbation by nilpotent operator, Spectrum
Junli Shen; Fei Zuo; Alatancang Chen. Some results on higher order symmetric operators. Filomat, Tome 37 (2023) no. 12, p. 3769 . doi: 10.2298/FIL2312769S
@article{10_2298_FIL2312769S,
author = {Junli Shen and Fei Zuo and Alatancang Chen},
title = {Some results on higher order symmetric operators},
journal = {Filomat},
pages = {3769 },
year = {2023},
volume = {37},
number = {12},
doi = {10.2298/FIL2312769S},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2312769S/}
}
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