Extension of operators on spaces of vector-valued continuous functions
Let X be a completely regular Hausdorff space and let Ba stand for the Baire σ-algebra of sets in X. For a Banach space E let Crc(X,E) be the space of all continuous functions f:X→E such that f(X) is a relatively compact set in E, and let B(Ba,E) be the space of all totally Ba-measurable functions f...
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| Published in: | Indagationes mathematicae Vol. 27; no. 1; pp. 20 - 28 |
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| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
01.01.2016
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| ISSN: | 0019-3577, 1872-6100 |
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| Abstract | Let X be a completely regular Hausdorff space and let Ba stand for the Baire σ-algebra of sets in X. For a Banach space E let Crc(X,E) be the space of all continuous functions f:X→E such that f(X) is a relatively compact set in E, and let B(Ba,E) be the space of all totally Ba-measurable functions f:X→E. For a Banach space Y we study the problem of extension of some natural classes of bounded linear operators T:Crc(X,E)→Y to operators T¯:B(Ba,E)→Y. |
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| AbstractList | Let X be a completely regular Hausdorff space and let Ba stand for the Baire σ-algebra of sets in X. For a Banach space E let Crc(X,E) be the space of all continuous functions f:X→E such that f(X) is a relatively compact set in E, and let B(Ba,E) be the space of all totally Ba-measurable functions f:X→E. For a Banach space Y we study the problem of extension of some natural classes of bounded linear operators T:Crc(X,E)→Y to operators T¯:B(Ba,E)→Y. |
| Author | Nowak, Marian |
| Author_xml | – sequence: 1 givenname: Marian surname: Nowak fullname: Nowak, Marian email: M.Nowak@wmie.uz.zgora.pl organization: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, ul. Szafrana 4A, 65–516 Zielona Góra, Poland |
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| Cites_doi | 10.1090/S0002-9947-1976-0390733-9 10.1016/j.indag.2011.11.001 10.2140/pjm.1975.56.547 10.21136/CMJ.1971.101000 10.1090/S0002-9947-1975-0365111-8 10.1016/j.indag.2012.02.004 10.7146/math.scand.a-11003 10.1090/S0002-9947-1978-0492297-X 10.1090/S0002-9947-1974-0338821-5 10.4134/JKMS.2015.52.1.177 10.1002/mana.19760710117 |
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| Copyright | 2015 Royal Dutch Mathematical Society (KWG) |
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| Keywords | Strict topologies Vector measures Spaces of vector-valued continuous functions Integration operators |
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| References | Hoffmann-Jörgënsen (br000040) 1971; 28 Nowak (br000090) 2012; 23 Katsaras (br000055) 1975; 206 Katsaras (br000060) 1976; 71 Brooks, Lewis (br000015) 1972; 192 Katsaras (br000050) 1974; 15 Nowak (br000095) 2015; 52 Dinculeanu (br000025) 1967 Batt (br000010) 1969; 14 Katsaras, Liu (br000070) 1975; 56 Lewis (br000080) 1970; 14 Wheeler (br000100) 1983; 2 Dinculeanu (br000030) 2000 Aliprantis, Burkinshaw (br000005) 1985 Kantorovitch, Akilov (br000045) 1982 Diestel, Uhl (br000020) 1977; vol. 15 Khurana (br000075) 1978; 241 Dobrakov (br000035) 1971; 21 Katsaras (br000065) 1976; 216 Nowak (br000085) 2012; 23 Nowak (10.1016/j.indag.2015.07.003_br000085) 2012; 23 Nowak (10.1016/j.indag.2015.07.003_br000090) 2012; 23 Kantorovitch (10.1016/j.indag.2015.07.003_br000045) 1982 Nowak (10.1016/j.indag.2015.07.003_br000095) 2015; 52 Dinculeanu (10.1016/j.indag.2015.07.003_br000025) 1967 Batt (10.1016/j.indag.2015.07.003_br000010) 1969; 14 Aliprantis (10.1016/j.indag.2015.07.003_br000005) 1985 Katsaras (10.1016/j.indag.2015.07.003_br000055) 1975; 206 Katsaras (10.1016/j.indag.2015.07.003_br000060) 1976; 71 Wheeler (10.1016/j.indag.2015.07.003_br000100) 1983; 2 Dinculeanu (10.1016/j.indag.2015.07.003_br000030) 2000 Katsaras (10.1016/j.indag.2015.07.003_br000050) 1974; 15 Lewis (10.1016/j.indag.2015.07.003_br000080) 1970; 14 Dobrakov (10.1016/j.indag.2015.07.003_br000035) 1971; 21 Brooks (10.1016/j.indag.2015.07.003_br000015) 1972; 192 Khurana (10.1016/j.indag.2015.07.003_br000075) 1978; 241 Diestel (10.1016/j.indag.2015.07.003_br000020) 1977; vol. 15 Hoffmann-Jörgënsen (10.1016/j.indag.2015.07.003_br000040) 1971; 28 Katsaras (10.1016/j.indag.2015.07.003_br000065) 1976; 216 Katsaras (10.1016/j.indag.2015.07.003_br000070) 1975; 56 |
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| Snippet | Let X be a completely regular Hausdorff space and let Ba stand for the Baire σ-algebra of sets in X. For a Banach space E let Crc(X,E) be the space of all... |
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| SubjectTerms | Integration operators Spaces of vector-valued continuous functions Strict topologies Vector measures |
| Title | Extension of operators on spaces of vector-valued continuous functions |
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