×

zbMATH — the first resource for mathematics

A note on compact operators on matrix domains. (English) Zbl 1147.47002
The authors establish some identities or estimates for the operator norms and Hausdorff measures of noncompactness of linear operators given by infinite matrices on some matrix domains. Characterizations of compact operators on some matrix domains are also obtained.

MSC:
47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
40H05 Functional analytic methods in summability
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Altay, B.; Başar, F., On the paranormed Riesz sequence spaces of non-absolute type, Southeast Asian bull. math., 26, 5, 701-715, (2002) · Zbl 1058.46002
[2] Altay, B.; Başar, F., Some Euler sequence spaces of non-absolute type, Ukrainian math. J., 57, 1, 1-17, (2005) · Zbl 1096.46011
[3] Altay, B.; Başar, F.; Mursaleen, On the Euler sequence spaces which include the spaces \(\ell_p\) and \(\ell_\infty\) I, Inform. sci., 176, 10, 1450-1462, (2006) · Zbl 1101.46015
[4] Başar, F.; Şengönul, M., Some new Cesàro sequence spaces of non-absolute type, Soochow J. math., 31, 1, 107-119, (2005) · Zbl 1085.46500
[5] Cooke, R.C., Infinite matrices and sequence spaces, (1950), Macmillan & Co. London · Zbl 0040.02501
[6] Jarrah, A.M.; Malkowsky, E., Ordinary, absolute and strong summability and matrix transformations, Filomat, 17, 59-78, (2003) · Zbl 1274.40001
[7] Djolović, I., Compact operators on the spaces \(a_0^r(\operatorname{\Delta})\) and \(a_c^r(\operatorname{\Delta})\), J. math. anal. appl., 318, 2, 658-666, (2006) · Zbl 1099.47021
[8] Djolović, I., On the space of bounded Euler difference sequences and some classes of compact operators, Appl. math. comput., 182, 2, 1803-1811, (2006) · Zbl 1111.46004
[9] Kızmaz, H., On certain sequence spaces, Canad. math. bull., 24, 169-176, (1981) · Zbl 0454.46010
[10] Malkowsky, E., Klassen von matrixabbildungen in paranormierten FK-Räumen, Analysis, 7, 275-292, (1987) · Zbl 0653.40005
[11] Malkowsky, E.; Rakočević, V., An introduction into the theory of sequence spaces and measures of noncompactness, Zb. rad. (beogr.), 9, 17, 143-234, (2000) · Zbl 0996.46006
[12] Malkowsky, E.; Rakočević, V., On matrix domains of triangles, Appl. math. comput., 189, 2, 1146-1163, (2007) · Zbl 1132.46011
[13] Mursaleen; Altay, B.; Başar, F., On the Euler sequence spaces which include the spaces \(\ell_p\) and \(\ell_\infty\) II, Nonlinear anal., 65, 3, 707-717, (2006) · Zbl 1108.46019
[14] Ng, P.-N.; Lee, P.-Y., Cesàro sequence spaces of non-absolute type, Comment. math. prace mat., 20, 2, 429-433, (1978) · Zbl 0408.46012
[15] Rakočević, V., Measures of noncompactness and some applications, Filomat, 12, 87-120, (1998) · Zbl 1009.47047
[16] Sirajudeen, S.M., Matrix transformations of bv into ℓ(q), ℓ∞(q), c0(q), and c(q), Indian J. pure appl. math., 23, 1, 55-61, (1992) · Zbl 0767.40003
[17] Wang, C.-S., On Nörlund sequence spaces, Tamkang J. math., 9, 269-279, (1978)
[18] Wilansky, A., Functional analysis, (1964), Blaisdell New York-Toronto-London · Zbl 0136.10603
[19] Wilansky, A., Summability through functional analysis, North-holland math. stud., vol. 85, (1984), Amsterdam · Zbl 0531.40008
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.