Title: | Isomorphic properties in spaces of compact operators (English) |
Author: | Ghenciu, Ioana |
Language: | English |
Journal: | Commentationes Mathematicae Universitatis Carolinae |
ISSN: | 0010-2628 (print) |
ISSN: | 1213-7243 (online) |
Volume: | 64 |
Issue: | 2 |
Year: | 2023 |
Pages: | 175-184 |
Summary lang: | English |
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Category: | math |
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Summary: | We introduce the definition of $p$-limited completely continuous operators, $1\le p<\infty$. The question of whether a space of operators has the property that every $p$-limited subset is relative compact when the dual of the domain and the codomain have this property is studied using $p$-limited completely continuous evaluation operators. (English) |
Keyword: | $p$-limited set |
Keyword: | limited set |
Keyword: | space of compact operators |
MSC: | 46B20 |
MSC: | 46B25 |
MSC: | 46B28 |
idZBL: | Zbl 07790590 |
idMR: | MR4658998 |
DOI: | 10.14712/1213-7243.2023.026 |
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Date available: | 2023-12-13T13:36:06Z |
Last updated: | 2024-02-13 |
Stable URL: | http://hdl.handle.net/10338.dmlcz/151862 |
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Reference: | [1] Bahreini M., Bator E., Ghenciu I.: Complemented subspaces of linear bounded operators.Canad. Math. Bull. 55 (2012), no. 3, 449–461. MR 2957262, 10.4153/CMB-2011-097-2 |
Reference: | [2] Bourgain J.: New Classes of $\mathcal{L}_p$-spaces.Lecture Notes in Mathematics, 889, Springer, Berlin, 1981. MR 0639014 |
Reference: | [3] Bourgain J., Diestel J.: Limited operators and strict cosingularity.Math. Nachr. 119 (1984), 55–58. Zbl 0601.47019, MR 0774176, 10.1002/mana.19841190105 |
Reference: | [4] Cilia R., Emmanuele G.: Some isomorphic properties in $K(X, Y)$ and in projective tensor products.Colloq. Math. 146 (2017), no. 2, 239–252. MR 3622375, 10.4064/cm6184-12-2015 |
Reference: | [5] Delgado J. M., Piñeiro C.: A note on $p$-limited sets.J. Math. Appl. 410 (2014), no. 2, 713–718. MR 3111861 |
Reference: | [6] Diestel J.: A survey of results related to the Dunford–Pettis property.Proc. of the Conf. on Integration, Topology, and Geometry in Linear Spaces, Univ. North Carolina, Chapel Hill, N.C., 1979, Contemp. Math., 2, American Mathematical Society, Providence, 1980, pages 15–60. MR 0621850 |
Reference: | [7] Diestel J.: Sequences and Series in Banach Spaces.Graduate Texts in Mathematics, 92, Springer, New York, 1984. MR 0737004 |
Reference: | [8] Diestel J., Jarchow H., Tonge A.: Absolutely Summing Operators.Cambridge Studies in Advanced Mathematics, 43, Cambridge University Press, Cambridge, 1995. Zbl 1139.47021, MR 1342297 |
Reference: | [9] Diestel J., Uhl J. J., Jr.: Vector Measures.Mathematical Surveys, 15, American Mathematical Society, Providence, 1977. Zbl 0521.46035, MR 0453964 |
Reference: | [10] Drewnowski L., Emmanuele G.: On Banach spaces with the Gel'fand–Phillips property. II.Rend. Circ. Mat. Palermo (2) 38 (1989), no. 3, 377–391. MR 1053378, 10.1007/BF02850021 |
Reference: | [11] Emmanuele G.: A dual characterization of Banach spaces not containing $l^1$.Bull. Polish Acad. Sci. Math. 34 (1986), no. 3–4, 155–160. MR 0861172 |
Reference: | [12] Emmanuele G.: Banach spaces in which Dunford–Pettis sets are relatively compact.Arch. Math. (Basel) 58 (1992), no. 5, 477–485. MR 1156580, 10.1007/BF01190118 |
Reference: | [13] Fourie J. H., Zeekoei E. D.: On weak-star $p$-convergent operators.Quaest. Math. 40 (2017), no. 5, 563–579. MR 3691468, 10.2989/16073606.2017.1301591 |
Reference: | [14] Ghenciu I.: A note on relative compactness in $K(X,Y)$.Ann. Funct. Anal. 7 (2016), no. 3, 470–483. MR 3528378, 10.1215/20088752-3624814 |
Reference: | [15] Ghenciu I.: Dunford–Pettis like properties on tensor products.Quaest. Math. 41 (2018), 811–828. MR 3857131, 10.2989/16073606.2017.1402383 |
Reference: | [16] Ghenciu I.: A note on $p$-limited sets in dual Banach spaces.Monatsh. Math. 200 (2023), no. 2, 255–270. MR 4544297, 10.1007/s00605-022-01738-6 |
Reference: | [17] Ghenciu I., Lewis P.: The Dunford–Pettis property, the Gelfand–Phillips property, and $L$-sets.Colloq. Math. 106 (2006), no. 2, 311–324. MR 2283818, 10.4064/cm106-2-11 |
Reference: | [18] Ghenciu I., Lewis P.: The embeddability of $c_0$ in spaces of operators.Bull. Pol. Acad. Sci. Math. 56 (2008), no. 3–4, 239–256. Zbl 1167.46016, MR 2481977, 10.4064/ba56-3-7 |
Reference: | [19] Karn A. K., Sinha D. P.: An operator summability of sequences in Banach spaces.Glasg. Math. J. 56 (2014), no. 2, 427–437. MR 3187909, 10.1017/S0017089513000360 |
Reference: | [20] Palmer T. W.: Totally bounded sets of precompact linear operators.Proc. Amer. Math. Soc. 20 (1969), 101–106. MR 0235425, 10.1090/S0002-9939-1969-0235425-3 |
Reference: | [21] Pełczyński A., Semadeni Z.: Spaces of continuous functions. III. Spaces $C(\Omega)$ for $\Omega$ without perfect subsets.Studia Math. 18 (1959), 211–222. MR 0107806, 10.4064/sm-18-2-211-222 |
Reference: | [22] Ruess W.: Duality and geometry of spaces of compact operators.Functional Analysis: Surveys and Recent Results, III, Paderborn, 1983, North-Holland Math. Stud., 90, Notas Mat., 94, North-Holland Publishing Co., Amsterdam, 1984, pages 59–78. Zbl 0573.46007, MR 0761373 |
Reference: | [23] Salimi M., Mostaghioun S. M.: The Gelfand–Phillips property in closed subspaces of some operator spaces.Banach J. Math. Anal. 5 (2011), no. 2, 84–92. MR 2792501, 10.15352/bjma/1313363004 |
Reference: | [24] Schlumprecht T.: Limited Sets in Banach Spaces.Ph.D. Dissertation, Ludwigs-Maxmilians-Universität, Münich, 1987. |
Reference: | [25] Wen Y., Chen J.: Characterizations of Banach spaces with relatively compact Dunford–Pettis sets.Adv. Math. (China) 45 (2016), no. 1, 122–132. MR 3483491 |
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