×

Cyclicity of special operators on a BK with AK space. (English) Zbl 1334.47030

Summary: Let \(\Omega\) be a complex domain and let \(F\) be a reflexive BK space with AK such that \(\hat{F} \subset H(\Omega)\) and the functional of evaluation at \(\lambda\) is bounded for all \(\lambda \in \Omega\). We will investigate the cyclicity for the adjoint of a weighted composition operator acting on \(\hat{F}\).

MSC:

47B33 Linear composition operators
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Wilansky, A., Summability through Functional Analysis. Summability through Functional Analysis, Mathematics Studies 85 (1984), North-Holland · Zbl 0531.40008
[2] Malkowsky, E., Linear operators in certain BK spaces, Bolyai Society Mathematical Studies, 5, 259-273 (1996) · Zbl 0861.40007
[3] Ould Sidaty, M. A., Reflexivity and AK-property of certain vector sequence spaces, Bulletin of the Belgian Mathematical Society, 10, 4, 579-583 (2003) · Zbl 1070.46011
[4] Aydin, C.; Başar, F., On the new sequence spaces which include the spaces \(c_0\) and \(c\), Hokkaido Mathematical Journal, 33, 2, 383-398 (2004) · Zbl 1085.46002 · doi:10.14492/hokmj/1285766172
[5] Aydin, C.; Basar, F., Some new sequence spaces which include the spaces \(l_p\) and \(l_\infty \), Demonstratio Mathematica, 38, 3, 641-656 (2005) · Zbl 1096.46005
[6] Malafosse, B. D., The Banach algebra \(B(X)\) and Applications, where \(X\) is a BK space, Matematički Vesnik, 57, 41-60 (2005) · Zbl 1112.46004
[7] Mursaleen, M.; Noman, A. K., On some new difference sequence spaces of non-absolute type, Mathematical and Computer Modelling, 52, 3-4, 603-617 (2010) · Zbl 1201.40003 · doi:10.1016/j.mcm.2010.04.006
[8] Mursaleen, M.; Noman, A. K., Applications of the Hausdorff measure of noncompactness in some sequence spaces of weighted means, Computers & Mathematics with Applications, 60, 5, 1245-1258 (2010) · Zbl 1201.40002 · doi:10.1016/j.camwa.2010.06.005
[9] Mursaleen, M.; Noman, A. K., Compactness by the Hausdorff measure of noncompactness, Nonlinear Analysis, 73, 8, 2541-2557 (2010) · Zbl 1211.47061 · doi:10.1016/j.na.2010.06.030
[10] Mursaleen, M.; Noman, A. K., The Hausdorff measure of noncompactness of matrix operators on some BK spaces, Operators and Matrices, 5, 3, 473-486 (2011) · Zbl 1227.47032 · doi:10.7153/oam-05-35
[11] Basarir, M.; Kara, E. E., On compact operators on the Riesz \(B^m\)-difference sequences, Iranian Journal of Science and Technology, 3, 371-376 (2012) · Zbl 1367.47025
[12] Malkowsky, E., Characterization of compact operators between certain BK spaces, Filomat, 27, 3, 447-457 (2013) · Zbl 1324.40013 · doi:10.2298/fil1303447m
[13] Malkowsky, E., Measure of noncompactness for compact matrix operators on some BK spaces, Filomat, 28, 5, 1081-1086 (2014) · Zbl 1466.47023 · doi:10.2298/fil1405081a
[14] Kirisci, M., The sequence space bv and some applications, Mathematica Aeterna, 4, 3, 207-223 (2014)
[15] Bagheri, L.; Yousefi, B., Reflexivity of the shift operator on some BK spaces, Rendiconti del Circolo Matematico di Palermo, 63, 1, 91-96 (2014) · Zbl 1309.47034 · doi:10.1007/s12215-013-0143-5
[16] Kamali, Z.; Khani Robati, B.; Hedayatian, K., Cyclicity of the adjoint of weighted composition operators on the Hilbert space of analytic functions, Czechoslovak Mathematical Journal, 61, 2, 551-563 (2011) · Zbl 1243.47022 · doi:10.1007/s10587-011-0074-2
[17] Shu-Hong, W. U., Cyclic behavior for adjoint operators of composition operators on the weighted Hardy space, Guangxi Sciences, 15, 4, 139-151 (2008)
[18] Zhao, L., Unitary weighted composition operators on the Fock space of \(c^n\), Complex Analysis and Operator Theory, 8, 2, 581-590 (2014) · Zbl 1303.47031 · doi:10.1007/s11785-013-0313-7
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.