On \(m\)-skew complex symmetric operators
-
2912
Downloads
-
4683
Views
Authors
Haiying Li
- School of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, Henan, P. R. China.
Yaru Wang
- School of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, Henan, P. R. China.
Abstract
In this paper, the definition of \(m\)-skew complex symmetric operators is introduced. Firstly, we
prove that \(\Delta_{m}^{-}(T)\) is complex symmetric with the
conjugation \(C\) and give some properties of \(\Delta_{m}^{-}(T)\).
Secondly, let \(T\) be \(m\)-skew complex symmetric
with conjugation \(C\), if \(n\) is odd, then \(T^{n}\) is \(m\)-skew complex symmetric
with conjugation \(C\); if \(n\) is even, with the assumption \(T^{*}CTC=CTCT^{*}\),
then \(T^{n}\) is \(m\)-complex symmetric
with conjugation \(C\). Finally, we give some properties of \(m\)-skew complex
symmetric operators.
Share and Cite
ISRP Style
Haiying Li, Yaru Wang, On \(m\)-skew complex symmetric operators, Journal of Nonlinear Sciences and Applications, 11 (2018), no. 6, 734--745
AMA Style
Li Haiying, Wang Yaru, On \(m\)-skew complex symmetric operators. J. Nonlinear Sci. Appl. (2018); 11(6):734--745
Chicago/Turabian Style
Li, Haiying, Wang, Yaru. "On \(m\)-skew complex symmetric operators." Journal of Nonlinear Sciences and Applications, 11, no. 6 (2018): 734--745
Keywords
- \(m\)-skew complex symmetric operator
- conjugation
- spectral
MSC
References
-
[1]
C. Benhida, K. Kliś-Garlicka, M. Ptak, Skew-symmetric operators and reflexivity, arXiv, 2016 (2016), 7 pages.
-
[2]
M. Cho, E. Ko, J. E. Lee, On m-complex symmetric operators, Mediter. J. Math., 13 (2016), 2025–2038.
-
[3]
M. Cho, E. Ko, J. E. Lee, On m-complex symmetric operators II, Mediter. J. Math., 13 (2016), 3255–3264.
-
[4]
M. Cho, E. Ko, J. E. Lee, Properties of m-complex symmetric operators, Stud. Univ. Babeş-Bolyai Math., 62 (2017), 233–248.
-
[5]
J. B. Conway, A course in functional analysis, Second edition, Springer-Verlag, New York, (1990),
-
[6]
S. R. Garcia, E. Prodan, M. Putinar, Mathematical and physical aspects of complex symmetric operators, J. Phys. A, 2014 (2014), 54 pages.
-
[7]
S. R. Garcia, M. Putinar, Complex symmetric operators and applications, Trans. Amer. Math. Soc., 358 (2006), 1285– 1315.
-
[8]
P. V. Hai, L. H. Khoi, Complex symmetry of weighted composition operators on the Fock space, J. Math. Anal. Appl., 433 (2016), 1757–1771.
-
[9]
P. R. Halmos, A Hilbert Space Problem Book, Second edition, Springer-Verlag, New York-Berlin (1982)
-
[10]
J. W. Helton, Operators with a representation as multiplication by \(x\) on a Sobolev space, Colloquia Math. Soc. János Bolyai, North-Holland, Amsterdam (1972)
-
[11]
S. Jung, E. Ko, J. E. Lee, On complex symmetric operator matrices, J. Math. Anal. Appl., 406 (2013), 373–385.
-
[12]
S. Jung, E. Ko, M. Lee, J. Lee, On local spectral properties of complex symmetric operators, J. Math. Anal. Appl., 379 (2011), 325–333.
-
[13]
E. Ko, E. Ko, J. E. Lee, Skew complex symmetric operator and Weyl type theorems, Bull. Korean Math. Soc., 52 (2015), 1269–1283.
-
[14]
E. Ko, J. E. Lee, On complex symmetric Toeplitz operators, J. Math. Anal. Appl., 434 (2016), 20–34.
-
[15]
X. Wang, Z. Gao, A note on Aluthge transforms of complex symmetric operators and applications, Integral Equations Operator Theory, 65 (2009), 573–580.