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Yıl 2022, Cilt: 71 Sayı: 1, 204 - 211, 30.03.2022

Ulas Yamanci

https://doi.org/10.31801/cfsuasmas.926981

Öz

Kaynakça

  • Aronzajn, N., Theory of reproducing kernels, Trans. Amer. Math. Soc., 68 (1950), 337-404. https://doi.org/10.1090/S0002-9947-1950-0051437-7
  • Bakherad, M., Some Berezin number inequalities for operator matrices, Czech. Math. J., 68 (2018), 997-1009. https://doi.org/10.21136/CMJ.2018.0048-17
  • Bakherad, M., Garayev, M.T., Berezin number inequalities for operators, Concr. Oper., 6 (2019), 33-43. https://doi.org/10.1515/conop-2019-0003
  • Berezin, F.A., Covariant and contravariant symbols for operators, Math. USSR-Izv., 6 (1972), 1117-1151. https://doi.org/10.1070/IM1972v006n05ABEH001913
  • Das, N., Sahoo, M., A Generalization of Hardy-Hilbert’s Inequality for non-homogeneous kernel, Bul. Acad. S¸tiinte Repub. Mold. Mat., 3(67) (2011), 29-44.
  • Dragomir, S.S., A survey of some recent inequalities for the norm and numerical radius of operators in Hilbert spaces, Banach J. Math. Anal., 1(2) (2007), 154-175. https://doi.org/10.15352/bjma/1240336213
  • El-Haddad, M., Kittaneh, F., Numerical radius inequalities for Hilbert space operators II, Studia Math., 182 (2007), 133-140. https://doi.org/10.4064/sm182-2-3
  • Garayev, M.T., Gürdal, M., Okudan, A., Hardy-Hilbert’s inequality and a power inequality for Berezin numbers for operators, Math. Inequal. Appl., 3(19) (2016), 883-891. https://doi.org/10.7153/mia-19-64
  • Gustafson, K.E., Rao, D.K.M., Numerical Range, Springer Verlag, New York, 1997.
  • Hajmohamadi, M., Lashkaripour, R., Bakherad, M., Improvements of Berezin number inequalities, Linear Multilinear Algebra, 68(6) (2020), 1218-1229. https://doi.org/10.1080/03081087.2018.1538310
  • Hansen, F., Non-commutative Hardy inequalities, Bull. Lond. Math. Soc., 41(6) (2009), 1009-1016. https://doi.org/10.1112/blms/bdp078
  • Hansen, F., Krulic, K., Pecaric, J., Persson, L.-E., Generalized noncommutative Hardy and Hardy-Hilbert type inequalities, Internat. J. Math., 21(10) (2010), 1283-1295. https://doi.org/10.1142/S0129167X10006501
  • Hardy, G., Littlewood, J.E., Polya, G., Inequalities, 2 nd ed. Cambridge University Press, Cambridge, 1967.
  • Jarczyk, W., Matkowski, J., On Mulholland’s inequality, Proc. Amer. Math. Soc., 130 (2002), 3243-3247. https://doi.org/10.2307/1194150
  • Karaev, M.T., Berezin symbol and invertibility of operators on the functional Hilbert spaces, J. Funct. Anal., 238 (2006), 181-192. https://doi.org/10.1016/j.jfa.2006.04.030
  • Karaev, M.T., Reproducing kernels and Berezin symbols techniques in various questions of operator theory, Complex Anal. Oper. Theory, 7 (2013), 983-1018. https://doi.org/10.1007/s11785-012-0232-z
  • Kian, M., Hardy-Hilbert type inequalities for Hilbert space operators, Ann. Funct. Anal., 3(2)(2012), 128-134. https://doi.org/10.15352/afa/1399899937
  • Kittaneh, F., Numerical radius inequalities for Hilbert space operators, Studia Math., 168 (2005), 73-80.
  • Kittaneh, F., Moslehian, M.S., Yamazaki, T., Cartesian decomposition and numerical radius inequalities, Linear Algebra Appl., 471 (2015), 46-53. https://doi.org/10.1016/j.laa.2014.12.016
  • Mulholland, H. P., A further generalization of Hilbert double series theorem, J. London Math. Soc., 6 (1931), 100-106. https://doi.org/10.1112/jlms/s1-6.2.100
  • Sahoo, S., Das, N., Mishra, D., Numerical radius inequalities for operator matrices, Adv Oper. Theory, 4(1) (2019), 197-214. https://doi.org/10.15352/aot.1804-1359
  • Sahoo, S., Das, N., Mishra, D., Berezin number and numerical radius inequalities for operators on Hilbert spaces, Adv. Oper. Theory, 5 (2020), 714-727. https://doi.org/10.1007/s43036-019- 00035-8
  • Saitoh, S., Sawano, Y., Theory of reproducing kernels and applications, Springer, 2016.
  • Yamancı, U., Gürdal, M., On numerical radius and Berezin number inequalities for reproducing kernel Hilbert space, New York J. Math., 23 (2017), 1531-1537.
  • Yamancı, U., Gürdal, M., Garayev, M.T., Berezin number inequality for convex function in reproducing kernel Hilbert space, Filomat, 31(18) (2017), 5711-5717. https://doi.org/10.2298/FIL1718711Y
  • Yamancı, U., Garayev, M., Some results related to the Berezin number inequalities, Turk. J. Math., 43(4) (2019), 1940-1952. https://doi.org/10.3906/mat-1812-12
  • Yamancı, U., Garayev, M., Celik, C., Hardy-Hilbert type inequality in reproducing kernel Hilbert space: its applications and related results, Linear Multilinear Algebra, 67(4) (2019), 830-842. https://doi.org/10.1080/03081087.2018.1490688
  • Yamancı, U., Tunç, R., Gürdal, M., Berezin number, Grüss-type inequalities and their applications, Bull. Malays. Math. Sci. Soc., 43(3) (2020), 2287-2296. https://doi.org/10.1007/s40840-019-00804-x
  • Yang, B., A new half-discrete Mulholland-type inequality with parameters, Ann. Funct. Anal., 3(1) (2012), 142-150. https://doi.org/10.15352/afa/1399900031

Operator inequalities in reproducing kernel Hilbert spaces

Yıl 2022, Cilt: 71 Sayı: 1, 204 - 211, 30.03.2022

Ulas Yamanci

https://doi.org/10.31801/cfsuasmas.926981

Öz

In this paper, by using some classical Mulholland type inequality, Berezin symbols and reproducing kernel technique, we prove the power inequalities for the Berezin number $ber(A)$ for some self-adjoint operators $A$ on ${H}(\Omega )$.  Namely, some Mulholland type inequality for reproducing kernel Hilbert space operators are established. By applying this inequality, we prove that $(ber(A))^{n}\leq C_{1}ber(A^{n})$ for any positive operator $A$ on ${H}(\Omega )$.

Anahtar Kelimeler

Mulholland type inequality Berezin number positive operator reproducing kernel Hilbert space Berezin symbol

Kaynakça

  • Aronzajn, N., Theory of reproducing kernels, Trans. Amer. Math. Soc., 68 (1950), 337-404. https://doi.org/10.1090/S0002-9947-1950-0051437-7
  • Bakherad, M., Some Berezin number inequalities for operator matrices, Czech. Math. J., 68 (2018), 997-1009. https://doi.org/10.21136/CMJ.2018.0048-17
  • Bakherad, M., Garayev, M.T., Berezin number inequalities for operators, Concr. Oper., 6 (2019), 33-43. https://doi.org/10.1515/conop-2019-0003
  • Berezin, F.A., Covariant and contravariant symbols for operators, Math. USSR-Izv., 6 (1972), 1117-1151. https://doi.org/10.1070/IM1972v006n05ABEH001913
  • Das, N., Sahoo, M., A Generalization of Hardy-Hilbert’s Inequality for non-homogeneous kernel, Bul. Acad. S¸tiinte Repub. Mold. Mat., 3(67) (2011), 29-44.
  • Dragomir, S.S., A survey of some recent inequalities for the norm and numerical radius of operators in Hilbert spaces, Banach J. Math. Anal., 1(2) (2007), 154-175. https://doi.org/10.15352/bjma/1240336213
  • El-Haddad, M., Kittaneh, F., Numerical radius inequalities for Hilbert space operators II, Studia Math., 182 (2007), 133-140. https://doi.org/10.4064/sm182-2-3
  • Garayev, M.T., Gürdal, M., Okudan, A., Hardy-Hilbert’s inequality and a power inequality for Berezin numbers for operators, Math. Inequal. Appl., 3(19) (2016), 883-891. https://doi.org/10.7153/mia-19-64
  • Gustafson, K.E., Rao, D.K.M., Numerical Range, Springer Verlag, New York, 1997.
  • Hajmohamadi, M., Lashkaripour, R., Bakherad, M., Improvements of Berezin number inequalities, Linear Multilinear Algebra, 68(6) (2020), 1218-1229. https://doi.org/10.1080/03081087.2018.1538310
  • Hansen, F., Non-commutative Hardy inequalities, Bull. Lond. Math. Soc., 41(6) (2009), 1009-1016. https://doi.org/10.1112/blms/bdp078
  • Hansen, F., Krulic, K., Pecaric, J., Persson, L.-E., Generalized noncommutative Hardy and Hardy-Hilbert type inequalities, Internat. J. Math., 21(10) (2010), 1283-1295. https://doi.org/10.1142/S0129167X10006501
  • Hardy, G., Littlewood, J.E., Polya, G., Inequalities, 2 nd ed. Cambridge University Press, Cambridge, 1967.
  • Jarczyk, W., Matkowski, J., On Mulholland’s inequality, Proc. Amer. Math. Soc., 130 (2002), 3243-3247. https://doi.org/10.2307/1194150
  • Karaev, M.T., Berezin symbol and invertibility of operators on the functional Hilbert spaces, J. Funct. Anal., 238 (2006), 181-192. https://doi.org/10.1016/j.jfa.2006.04.030
  • Karaev, M.T., Reproducing kernels and Berezin symbols techniques in various questions of operator theory, Complex Anal. Oper. Theory, 7 (2013), 983-1018. https://doi.org/10.1007/s11785-012-0232-z
  • Kian, M., Hardy-Hilbert type inequalities for Hilbert space operators, Ann. Funct. Anal., 3(2)(2012), 128-134. https://doi.org/10.15352/afa/1399899937
  • Kittaneh, F., Numerical radius inequalities for Hilbert space operators, Studia Math., 168 (2005), 73-80.
  • Kittaneh, F., Moslehian, M.S., Yamazaki, T., Cartesian decomposition and numerical radius inequalities, Linear Algebra Appl., 471 (2015), 46-53. https://doi.org/10.1016/j.laa.2014.12.016
  • Mulholland, H. P., A further generalization of Hilbert double series theorem, J. London Math. Soc., 6 (1931), 100-106. https://doi.org/10.1112/jlms/s1-6.2.100
  • Sahoo, S., Das, N., Mishra, D., Numerical radius inequalities for operator matrices, Adv Oper. Theory, 4(1) (2019), 197-214. https://doi.org/10.15352/aot.1804-1359
  • Sahoo, S., Das, N., Mishra, D., Berezin number and numerical radius inequalities for operators on Hilbert spaces, Adv. Oper. Theory, 5 (2020), 714-727. https://doi.org/10.1007/s43036-019- 00035-8
  • Saitoh, S., Sawano, Y., Theory of reproducing kernels and applications, Springer, 2016.
  • Yamancı, U., Gürdal, M., On numerical radius and Berezin number inequalities for reproducing kernel Hilbert space, New York J. Math., 23 (2017), 1531-1537.
  • Yamancı, U., Gürdal, M., Garayev, M.T., Berezin number inequality for convex function in reproducing kernel Hilbert space, Filomat, 31(18) (2017), 5711-5717. https://doi.org/10.2298/FIL1718711Y
  • Yamancı, U., Garayev, M., Some results related to the Berezin number inequalities, Turk. J. Math., 43(4) (2019), 1940-1952. https://doi.org/10.3906/mat-1812-12
  • Yamancı, U., Garayev, M., Celik, C., Hardy-Hilbert type inequality in reproducing kernel Hilbert space: its applications and related results, Linear Multilinear Algebra, 67(4) (2019), 830-842. https://doi.org/10.1080/03081087.2018.1490688
  • Yamancı, U., Tunç, R., Gürdal, M., Berezin number, Grüss-type inequalities and their applications, Bull. Malays. Math. Sci. Soc., 43(3) (2020), 2287-2296. https://doi.org/10.1007/s40840-019-00804-x
  • Yang, B., A new half-discrete Mulholland-type inequality with parameters, Ann. Funct. Anal., 3(1) (2012), 142-150. https://doi.org/10.15352/afa/1399900031
Toplam 29 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Ulas Yamanci 0000-0002-4709-0993

Yayımlanma Tarihi 30 Mart 2022
Gönderilme Tarihi 24 Nisan 2021
Kabul Tarihi 26 Ağustos 2021
Yayımlandığı Sayı Yıl 2022 Cilt: 71 Sayı: 1

Kaynak Göster

APA Yamanci, U. (2022). Operator inequalities in reproducing kernel Hilbert spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 71(1), 204-211. https://doi.org/10.31801/cfsuasmas.926981
AMA Yamanci U. Operator inequalities in reproducing kernel Hilbert spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Mart 2022;71(1):204-211. doi:10.31801/cfsuasmas.926981
Chicago Yamanci, Ulas. “Operator Inequalities in Reproducing Kernel Hilbert Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71, sy. 1 (Mart 2022): 204-11. https://doi.org/10.31801/cfsuasmas.926981.
EndNote Yamanci U (01 Mart 2022) Operator inequalities in reproducing kernel Hilbert spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71 1 204–211.
IEEE U. Yamanci, “Operator inequalities in reproducing kernel Hilbert spaces”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 71, sy. 1, ss. 204–211, 2022, doi: 10.31801/cfsuasmas.926981.
ISNAD Yamanci, Ulas. “Operator Inequalities in Reproducing Kernel Hilbert Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71/1 (Mart 2022), 204-211. https://doi.org/10.31801/cfsuasmas.926981.
JAMA Yamanci U. Operator inequalities in reproducing kernel Hilbert spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71:204–211.
MLA Yamanci, Ulas. “Operator Inequalities in Reproducing Kernel Hilbert Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 71, sy. 1, 2022, ss. 204-11, doi:10.31801/cfsuasmas.926981.
Vancouver Yamanci U. Operator inequalities in reproducing kernel Hilbert spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71(1):204-11.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics

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