In this paper, the relation between q-deformed quasinormal operators and q-quasinormal operator classes is investigated. Moreover, we proof that these are same. Also, we consider the extended eigenvalue problems for bounded q-quasinormal operators.
[1] S. Ota, Some classes of q-deformed operators. J. Operator Theory 48 (2002), 151-186.
[2] S. Ota and F.K. Szafraniec , Notes on q-deformed operators. Studia Mathematica 165 (3)
(2004) , 295-301.
[3] S. Ota and F.K. Szafraniec, q-Positive definiteness and related operators. j. Math. Anal.
Appl. 329 (2007), 987-997.
[4] S. Ota, On q-deformed hyponormal operators. Math. Nachr. 248-249 (2003), 144-150.
[5] J. Cimpric, Y. Savchuk and K. Schmudgen, On q-normal operators and quantum complex
plane. Trans. Amer. Math. Soc. 366 (2014), 135-158.
[6] S. Lohaj, Quasi-normal operators. Int. Journal of Math. 4 (47) (2010), 2311-2320.
[7] J.B. Conway, The theory of subnormal operators. vol. 36. Providence, Rhode Island, USA,
American Mathematical Society (1985).
[8] A. Biswas, A. Lambert and S. Petrovic, Extended eigenvalues and Volterra operators. Glasgn
Math. J. 44 (2002), 521-534.
[9] A. Biswas and S. Petrovic, On extended eigenvalues of operators. Integr. Equat. Oper. Th.
57 (2007), 593-598.
[10] G. Cassier and H. Alkanjo, Extended spectrum and extended eigenspaces of quasi-normal
operators. Banach J. Math. Anal. 11 (2) (2017), 266-281.
[11] M. Sertbas and F. Yılmaz, On the extended spectrum of some quasinormal operators. Turk.
J. Math. 41 (2017), 1477-1481.
[12] M.T. Karaev, On extended eigenvalues and extended eigenvectors of some operator classes.
Proc. Amer. Math. Soc. 134 (8) (2006), 2383-2392.
[13] M. Gurdal, Description of extended eigenvalues and extended eigenvectors of integration
operator on the Wiener algebra. Expo. Math. 27 (2009), 153-160.
[14] M. Gurdal, On the extended eigenvalues and extended eigenvectors of shift operator on the
Wiener algebra. Appl. Math. Lett. 22 (11) (2009), 1727-1729.
[15] M. Gurdal, Connections between Deddens algebras and extended eigenvectors. Math. Notes.
90 (1) (2011), 37-40.
[16] M. Karaev, M. G¨urdal and S. Saltan, Some applications of Banach algebra techniques.
Math. Nachr. 284 (13) (2011), 1678-1689.
[1] S. Ota, Some classes of q-deformed operators. J. Operator Theory 48 (2002), 151-186.
[2] S. Ota and F.K. Szafraniec , Notes on q-deformed operators. Studia Mathematica 165 (3)
(2004) , 295-301.
[3] S. Ota and F.K. Szafraniec, q-Positive definiteness and related operators. j. Math. Anal.
Appl. 329 (2007), 987-997.
[4] S. Ota, On q-deformed hyponormal operators. Math. Nachr. 248-249 (2003), 144-150.
[5] J. Cimpric, Y. Savchuk and K. Schmudgen, On q-normal operators and quantum complex
plane. Trans. Amer. Math. Soc. 366 (2014), 135-158.
[6] S. Lohaj, Quasi-normal operators. Int. Journal of Math. 4 (47) (2010), 2311-2320.
[7] J.B. Conway, The theory of subnormal operators. vol. 36. Providence, Rhode Island, USA,
American Mathematical Society (1985).
[8] A. Biswas, A. Lambert and S. Petrovic, Extended eigenvalues and Volterra operators. Glasgn
Math. J. 44 (2002), 521-534.
[9] A. Biswas and S. Petrovic, On extended eigenvalues of operators. Integr. Equat. Oper. Th.
57 (2007), 593-598.
[10] G. Cassier and H. Alkanjo, Extended spectrum and extended eigenspaces of quasi-normal
operators. Banach J. Math. Anal. 11 (2) (2017), 266-281.
[11] M. Sertbas and F. Yılmaz, On the extended spectrum of some quasinormal operators. Turk.
J. Math. 41 (2017), 1477-1481.
[12] M.T. Karaev, On extended eigenvalues and extended eigenvectors of some operator classes.
Proc. Amer. Math. Soc. 134 (8) (2006), 2383-2392.
[13] M. Gurdal, Description of extended eigenvalues and extended eigenvectors of integration
operator on the Wiener algebra. Expo. Math. 27 (2009), 153-160.
[14] M. Gurdal, On the extended eigenvalues and extended eigenvectors of shift operator on the
Wiener algebra. Appl. Math. Lett. 22 (11) (2009), 1727-1729.
[15] M. Gurdal, Connections between Deddens algebras and extended eigenvectors. Math. Notes.
90 (1) (2011), 37-40.
[16] M. Karaev, M. G¨urdal and S. Saltan, Some applications of Banach algebra techniques.
Math. Nachr. 284 (13) (2011), 1678-1689.
Sertbaş, M., & Yılmaz, F. (2020). q-Quasinormal Operators and Its Extended Eigenvalues. Maltepe Journal of Mathematics, 2(1), 9-13.
AMA
Sertbaş M, Yılmaz F. q-Quasinormal Operators and Its Extended Eigenvalues. Maltepe Journal of Mathematics. April 2020;2(1):9-13.
Chicago
Sertbaş, Meltem, and Fatih Yılmaz. “q-Quasinormal Operators and Its Extended Eigenvalues”. Maltepe Journal of Mathematics 2, no. 1 (April 2020): 9-13.
EndNote
Sertbaş M, Yılmaz F (April 1, 2020) q-Quasinormal Operators and Its Extended Eigenvalues. Maltepe Journal of Mathematics 2 1 9–13.
IEEE
M. Sertbaş and F. Yılmaz, “q-Quasinormal Operators and Its Extended Eigenvalues”, Maltepe Journal of Mathematics, vol. 2, no. 1, pp. 9–13, 2020.
ISNAD
Sertbaş, Meltem - Yılmaz, Fatih. “q-Quasinormal Operators and Its Extended Eigenvalues”. Maltepe Journal of Mathematics 2/1 (April 2020), 9-13.
JAMA
Sertbaş M, Yılmaz F. q-Quasinormal Operators and Its Extended Eigenvalues. Maltepe Journal of Mathematics. 2020;2:9–13.
MLA
Sertbaş, Meltem and Fatih Yılmaz. “q-Quasinormal Operators and Its Extended Eigenvalues”. Maltepe Journal of Mathematics, vol. 2, no. 1, 2020, pp. 9-13.
Vancouver
Sertbaş M, Yılmaz F. q-Quasinormal Operators and Its Extended Eigenvalues. Maltepe Journal of Mathematics. 2020;2(1):9-13.