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$q$-Quasinormal Operators and Its Extended Eigenvalues

Yıl 2020, Cilt: 2 Sayı: 1, 9 - 13, 30.04.2020

Öz

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.

Kaynakça

  • [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.
  • [17] V.L. Ostrowski and Y.S. Samoilenko, Unbounded operators satisfying non-Lie commutation relations. Rep. Math. Phys. 28 (1989), 91-104.
  • [18] V.L. Ostrowski and Y.S. Samoilenko, Representations of quadratic ∗-algebras by bounded and unbounded operators. Rep. Math. Phys. 35 (1995), 283-301 .
Yıl 2020, Cilt: 2 Sayı: 1, 9 - 13, 30.04.2020

Öz

Kaynakça

  • [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.
  • [17] V.L. Ostrowski and Y.S. Samoilenko, Unbounded operators satisfying non-Lie commutation relations. Rep. Math. Phys. 28 (1989), 91-104.
  • [18] V.L. Ostrowski and Y.S. Samoilenko, Representations of quadratic ∗-algebras by bounded and unbounded operators. Rep. Math. Phys. 35 (1995), 283-301 .
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Meltem Sertbaş

Fatih Yılmaz 0000-0003-3317-6937

Yayımlanma Tarihi 30 Nisan 2020
Kabul Tarihi 28 Nisan 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 2 Sayı: 1

Kaynak Göster

APA 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. Nisan 2020;2(1):9-13.
Chicago Sertbaş, Meltem, ve Fatih Yılmaz. “$q$-Quasinormal Operators and Its Extended Eigenvalues”. Maltepe Journal of Mathematics 2, sy. 1 (Nisan 2020): 9-13.
EndNote Sertbaş M, Yılmaz F (01 Nisan 2020) $q$-Quasinormal Operators and Its Extended Eigenvalues. Maltepe Journal of Mathematics 2 1 9–13.
IEEE M. Sertbaş ve F. Yılmaz, “$q$-Quasinormal Operators and Its Extended Eigenvalues”, Maltepe Journal of Mathematics, c. 2, sy. 1, ss. 9–13, 2020.
ISNAD Sertbaş, Meltem - Yılmaz, Fatih. “$q$-Quasinormal Operators and Its Extended Eigenvalues”. Maltepe Journal of Mathematics 2/1 (Nisan 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 ve Fatih Yılmaz. “$q$-Quasinormal Operators and Its Extended Eigenvalues”. Maltepe Journal of Mathematics, c. 2, sy. 1, 2020, ss. 9-13.
Vancouver Sertbaş M, Yılmaz F. $q$-Quasinormal Operators and Its Extended Eigenvalues. Maltepe Journal of Mathematics. 2020;2(1):9-13.

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