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On matrix domains of triangles. (English) Zbl 1132.46011
The authors’ summary clearly explains the content of this paper: “We prove some general results for the determination of the \(\beta \)-duals of, and the characterisations of matrix transformations on matrix domains of arbitrary triangles in FK-spaces. Our results contain almost all recently published ones as special cases. We also study the measure of noncompactness of several matrix transformations. In particular, we obtain some known results of J. J. Sember [J. Lond. Math. Soc., II. Ser. 2, 530–534 (1970; Zbl 0199.11302)], give the corrected version of a recent result by I. Djolović [J. Math. Anal. Appl. 318, No. 2, 658–666 (2006; Zbl 1099.47021)], and study compact operators on some spaces of B. Altay, F. Başar and M. Mursaleen [Ukr. Mat. Zh. 57, No. 1, 3–17 (2005; Zbl 1096.46011); Inf. Sci. 176, No. 10, 1450–1462 (2006; Zbl 1101.46015); Nonlinear Anal., Theory Methods Appl. 65, No. 3(A), 707–717 (2006; Zbl 1108.46019)].”

MSC:
46B45 Banach sequence spaces
46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
46B07 Local theory of Banach spaces
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