Characterizations of Matrix and Compact Operators on BK Spaces

Yıl 2023, Cilt: 6 Sayı: 2, 76 - 85, 01.07.2023

Fadime Gökçe

https://doi.org/10.32323/ujma.1282831

Öz

In the present paper, by estimating operator norms, we give some characterizations of infinite matrix classes $\left( \left\vert E_{\mu }^{r}\right\vert _{q},\Lambda\right) $ and $\left( \left\vert E_{\mu }^{r}\right\vert _{\infty },\Lambda\right) $, where the absolute spaces $\ \left\vert E_{\mu }^{r}\right\vert _{q},$ $\left\vert E_{\mu }^{r}\right\vert _{\infty }$ have been recently studied by G\"{o}k\c{c}e and Sar{\i }g\"{o}l \cite{GS2019c} and $\Lambda$ is one of the well-known spaces $c_{0},c,l_{\infty },l_{q}(q\geq 1)$. Also, we obtain necessary and sufficient conditions for each matrix in these classes to be compact establishing their identities or estimates for the Hausdorff measures of noncompactness.

Anahtar Kelimeler

Absolute summability, Euler matrix, Hausdorff measures of noncompactness, Matrix transformations, Operator norm, Sequence spaces

Kaynakça

• [1] G. Perelman, The entropy formula for the Ricci flow and its geometric applications, Mathematics, (2002), 1–39.
• [2] G. Perelman, Ricci flow with surgery on three-manifolds, http://arXiv.org/abs/math/0303109, (2003), 1–22.
• [3] R. Sharma, Certain results on k-contact and (k;m)􀀀contact manifolds, J. Geom., 89 (2008), 138–147.
• [4] S. R. Ashoka, C. S. Bagewadi, G. Ingalahalli, Certain results on Ricci Solitons in a-Sasakian manifolds, Hindawi Publ. Corporation, Geometry, 2013, Article ID 573925, (2013), 4 Pages.
• [5] S. R. Ashoka, C. S. Bagewadi, G. Ingalahalli, A geometry on Ricci solitons in (LCS)n manifolds, Diff. Geom.-Dynamical Systems, 16 (2014), 50–62.
• [6] C. S. Bagewadi, G. Ingalahalli, Ricci solitons in Lorentzian-Sasakian manifolds, Acta Math. Acad. Paeda. Nyire., 28 (2012), 59–68.
• [7] G. Ingalahalli, C. S. Bagewadi, Ricci solitons in a-Sasakian manifolds, ISRN Geometry, 2012, Article ID 421384, (2012), 13 Pages.
• [8] C. L. Bejan, M. Crasmareanu, Ricci Solitons in manifolds with quasi-contact curvature, Publ. Math. Debrecen, 78 (2011), 235–243.
• [9] A. M. Blaga, h-Ricci solitons on para-kenmotsu manifolds, Balkan J. Geom. Appl., 20 (2015), 1–13.
• [10] S. Chandra, S. K. Hui, A. A. Shaikh, Second order parallel tensors and Ricci solitons on (LCS)n-manifolds, Commun. Korean Math. Soc., 30 (2015), 123–130.
• [11] B. Y. Chen, S. Deshmukh, Geometry of compact shrinking Ricci solitons, Balkan J. Geom. Appl., 19 (2014), 13–21.
• [12] S. Deshmukh, H. Al-Sodais, H. Alodan, A note on Ricci solitons, Balkan J. Geom. Appl., 16 (2011), 48–55.
• [13] C. He, M. Zhu, Ricci solitons on Sasakian manifolds, arxiv:1109.4407V2, [Math DG], (2011).
• [14] M. Atçeken, T. Mert, P. Uygun, Ricci-Pseudosymmetric (LCS)n􀀀manifolds admitting almost h􀀀Ricci solitons, Asian Journal of Math. and Computer Research, 29(2), (2022), 23–32.
• [15] H. Nagaraja, C. R. Premalatta, Ricci solitons in Kenmotsu manifolds, J. Math. Analysis, 3(2), (2012), 18–24.
• [16] M. M. Tripathi, Ricci solitons in contact metric manifolds, arxiv:0801,4221 V1, [Math DG], (2008).
• [17] D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Volume 203 of Progress in Mathematics, Birkhauser Boston, Inc., Boston, MA, USA, 2nd edition, 2010.
• [18] P. Alegre, D.E. Blair, A. Carriazo, Generalized Sasakian space form, Israel Journal of Mathematics, 141 (2004), 157–183.
• [19] P. Alegre, A. Carriazo, Semi-Riemannian generalized Sasakian space forms, Bulletin of the Malaysian Mathematical Sciences Society, 41(1) (2001), 1–14.
• [20] J. T Cho, M. Kimura, Ricci solitons and real hypersurfaces in a complex space form, Tohoku Math. J., 61 (2) (2009), 205–212.