Araştırma Makalesi
BibTex RIS Kaynak Göster

Polynomially partial isometric operators

Yıl 2023, Cilt: 52 Sayı: 1, 151 - 162, 15.02.2023

Dijana Mosic

https://doi.org/10.15672/hujms.1074783
Cited By: 1

Öz

In order to extend the notion of semi-generalized partial isometries and partial isometries, we introduce a new class of operators called polynomially partial isometries. Since this new class of operators contains semi-generalized partial isometries, partial isometries, isometries and co-isometries, we proposed a wider class of operators. Several basic properties of polynomially partial isometries and some invariant subspaces of corresponding operators are presented. We study decomposition theorems and spectral theorems for polynomially partial isometries, generalizing some well-known results for partial isometries and semi-generalized partial isometries to polynomially partial isometries. Applying polynomially partial isometries, we solve some equations.

Anahtar Kelimeler

partial isometry isometry decomposition theorem Hilbert space

Destekleyen Kurum

Ministry of Education, Science and Technological Development, Republic of Serbia

Proje Numarası

451-03-68/2022-14/200124

Kaynakça

  • [1] A. Alahmari, M. Mabrouk and M.A. Taoudi, Discussions on partial isometries in Banach spaces and Banach algebras, Bull. Korean Math. Soc. 54 (2), 485-495, 2017.
  • [2] S.A. Aluzuraiqi and A.B. Patel, On n-normal operators, General Math. Notes 1, 61-73, 2010.
  • [3] C. Apostol, Propriétés de certains operateurs bornés des espaces de Hilbert II, Rev. Roum. Math. Purs Appl. 12, 759-762, 1967.
  • [4] M.L. Arias and M. Mbekhta, On partial isometries in C*–algebras, Studia Math. 205 (1), 71-82, 2011.
  • [5] C. Badea and M. Mbekhta, Operators similar to partial isometries, Acta Sci. Math. (Szeged) 71, 663-680, 2005.
  • [6] S.K. Berberian, Approximate proper vectors, Proc. Amer. Math. Soc. 13, 111-114, 1962.
  • [7] M. Chō, J.E. Lee, K. Tanahashi and A. Uchiyama, Remarks on n-normal operators, Filomat 32 (15), 5441-5451, 2018.
  • [8] M. Chō and B. Načevska Nastovska, Spectral properties of n-normal operators, Filomat 32 (14), 5063-5069, 2018.
  • [9] D.S. Djordjević, M. Chō and D. Mosić, Polynomially normal operators, Ann. Funct. Anal. 11, 493-504, 2020.
  • [10] B.P. Duggal and I.H. Kim, On nth roots of normal operators, Filomat 34 (8), 2797- 2803, 2020.
  • [11] I. Erdelyi and F.R. Miller, Decomposition theorems for partial isometries, J. Math. Anal. Appl. 30, 665-679, 1970.
  • [12] F.J. Fernández-Polo and A. Peralta, Partial isometries: a survey, Adv. Oper. Theory 3 (1), 75-116, 2018.
  • [13] Z. Garbouj and H. Skhiri, Semi-generalized partial isometries operators, Results Math. 75, 15, 2020.
  • [14] P.R. Halmos and J.E. McLaughlin, Partial isometries, Pac. J. Appl. Math. 13, 585- 596, 1963.
  • [15] P.R. Halmos and L.J. Wallen, Powers of partial isometries, J. Math. Mech. 19, 657- 663, 1969/1970.
  • [16] O.A. Mahmoud Sid Ahmed, Generalization of m-partial isometries on a Hilbert space, Int. J. Pure Appl. Math. 104 (4), 599-619, 2015.
  • [17] M. Mbekhta, Partial isometries and generalized inverses, Acta Sci. Math. (Szeged) 70, 767-781, 2004.
  • [18] D. Mosić and D.S. Djordjević, Partial isometries and EP elements in Banach algebras, Abstr. Appl. Anal. 2011, Article ID 540212, 9 pages, 2011.
  • [19] D. Mosić and D.S. Djordjević, Weighted partial isometries and weighted–EP elements in C*-algebra, Appl. Math. Comput. 265, 17-30, 2015.
  • [20] A. Saddi and O.A. Mahmoud Sid Ahmed, m-partial isometries on Hilbert spaces, Internat. J. Functional Analysis, Operator Theory and Applications 2 (1), 67-83, 2010.
  • [21] C. Schmoeger, Partial isometries on Banach spaces, Seminar LV, No. 20, 13 pp. 28.02.2005.

Yıl 2023, Cilt: 52 Sayı: 1, 151 - 162, 15.02.2023

Dijana Mosic

https://doi.org/10.15672/hujms.1074783
Cited By: 1

Öz

Anahtar Kelimeler

partial isometry isometry decomposition theorem Hilbert space

Proje Numarası

451-03-68/2022-14/200124

Kaynakça

  • [1] A. Alahmari, M. Mabrouk and M.A. Taoudi, Discussions on partial isometries in Banach spaces and Banach algebras, Bull. Korean Math. Soc. 54 (2), 485-495, 2017.
  • [2] S.A. Aluzuraiqi and A.B. Patel, On n-normal operators, General Math. Notes 1, 61-73, 2010.
  • [3] C. Apostol, Propriétés de certains operateurs bornés des espaces de Hilbert II, Rev. Roum. Math. Purs Appl. 12, 759-762, 1967.
  • [4] M.L. Arias and M. Mbekhta, On partial isometries in C*–algebras, Studia Math. 205 (1), 71-82, 2011.
  • [5] C. Badea and M. Mbekhta, Operators similar to partial isometries, Acta Sci. Math. (Szeged) 71, 663-680, 2005.
  • [6] S.K. Berberian, Approximate proper vectors, Proc. Amer. Math. Soc. 13, 111-114, 1962.
  • [7] M. Chō, J.E. Lee, K. Tanahashi and A. Uchiyama, Remarks on n-normal operators, Filomat 32 (15), 5441-5451, 2018.
  • [8] M. Chō and B. Načevska Nastovska, Spectral properties of n-normal operators, Filomat 32 (14), 5063-5069, 2018.
  • [9] D.S. Djordjević, M. Chō and D. Mosić, Polynomially normal operators, Ann. Funct. Anal. 11, 493-504, 2020.
  • [10] B.P. Duggal and I.H. Kim, On nth roots of normal operators, Filomat 34 (8), 2797- 2803, 2020.
  • [11] I. Erdelyi and F.R. Miller, Decomposition theorems for partial isometries, J. Math. Anal. Appl. 30, 665-679, 1970.
  • [12] F.J. Fernández-Polo and A. Peralta, Partial isometries: a survey, Adv. Oper. Theory 3 (1), 75-116, 2018.
  • [13] Z. Garbouj and H. Skhiri, Semi-generalized partial isometries operators, Results Math. 75, 15, 2020.
  • [14] P.R. Halmos and J.E. McLaughlin, Partial isometries, Pac. J. Appl. Math. 13, 585- 596, 1963.
  • [15] P.R. Halmos and L.J. Wallen, Powers of partial isometries, J. Math. Mech. 19, 657- 663, 1969/1970.
  • [16] O.A. Mahmoud Sid Ahmed, Generalization of m-partial isometries on a Hilbert space, Int. J. Pure Appl. Math. 104 (4), 599-619, 2015.
  • [17] M. Mbekhta, Partial isometries and generalized inverses, Acta Sci. Math. (Szeged) 70, 767-781, 2004.
  • [18] D. Mosić and D.S. Djordjević, Partial isometries and EP elements in Banach algebras, Abstr. Appl. Anal. 2011, Article ID 540212, 9 pages, 2011.
  • [19] D. Mosić and D.S. Djordjević, Weighted partial isometries and weighted–EP elements in C*-algebra, Appl. Math. Comput. 265, 17-30, 2015.
  • [20] A. Saddi and O.A. Mahmoud Sid Ahmed, m-partial isometries on Hilbert spaces, Internat. J. Functional Analysis, Operator Theory and Applications 2 (1), 67-83, 2010.
  • [21] C. Schmoeger, Partial isometries on Banach spaces, Seminar LV, No. 20, 13 pp. 28.02.2005.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Dijana Mosic 0000-0002-3255-9322

Proje Numarası 451-03-68/2022-14/200124
Yayımlanma Tarihi 15 Şubat 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 52 Sayı: 1

Kaynak Göster

APA Mosic, D. (2023). Polynomially partial isometric operators. Hacettepe Journal of Mathematics and Statistics, 52(1), 151-162. https://doi.org/10.15672/hujms.1074783
AMA Mosic D. Polynomially partial isometric operators. Hacettepe Journal of Mathematics and Statistics. Şubat 2023;52(1):151-162. doi:10.15672/hujms.1074783
Chicago Mosic, Dijana. “Polynomially Partial Isometric Operators”. Hacettepe Journal of Mathematics and Statistics 52, sy. 1 (Şubat 2023): 151-62. https://doi.org/10.15672/hujms.1074783.
EndNote Mosic D (01 Şubat 2023) Polynomially partial isometric operators. Hacettepe Journal of Mathematics and Statistics 52 1 151–162.
IEEE D. Mosic, “Polynomially partial isometric operators”, Hacettepe Journal of Mathematics and Statistics, c. 52, sy. 1, ss. 151–162, 2023, doi: 10.15672/hujms.1074783.
ISNAD Mosic, Dijana. “Polynomially Partial Isometric Operators”. Hacettepe Journal of Mathematics and Statistics 52/1 (Şubat 2023), 151-162. https://doi.org/10.15672/hujms.1074783.
JAMA Mosic D. Polynomially partial isometric operators. Hacettepe Journal of Mathematics and Statistics. 2023;52:151–162.
MLA Mosic, Dijana. “Polynomially Partial Isometric Operators”. Hacettepe Journal of Mathematics and Statistics, c. 52, sy. 1, 2023, ss. 151-62, doi:10.15672/hujms.1074783.
Vancouver Mosic D. Polynomially partial isometric operators. Hacettepe Journal of Mathematics and Statistics. 2023;52(1):151-62.

Cited By

$$\Delta _{{{\varvec{i}}}_{g}}$$-invertible operators I
Acta Scientiarum Mathematicarum
https://doi.org/10.1007/s44146-024-00151-9

For more information about the journal, please visit: https://dergipark.org.tr/en/pub/hujms