Norm attaining bilinear forms on spaces of continuous functions. (English) Zbl 0926.46019
Summary: We show that continuous bilinear forms on spaces of continuous functions can be approximated by norm attaining bilinear forms.
MSC:
| 46B28 | Spaces of operators; tensor products; approximation properties |
| 46E15 | Banach spaces of continuous, differentiable or analytic functions |
| 47A58 | Linear operator approximation theory |
References:
| [1] | Bonsall, Numerical ranges II (1973) · doi:10.1017/CBO9780511662515 |
| [2] | DOI: 10.1006/jmaa.1997.5461 · Zbl 0888.46007 · doi:10.1006/jmaa.1997.5461 |
| [3] | Aron, Proc. 2nd Conf. on Function Spaces pp 19– (1995) |
| [4] | DOI: 10.1007/BF02761104 · Zbl 0852.46010 · doi:10.1007/BF02761104 |
| [5] | Schachermayer, Pac. J. Math. 105 pp 427– (1983) · Zbl 0458.46009 · doi:10.2140/pjm.1983.105.427 |
| [6] | Rudin, Real and complex analysis (1966) |
| [7] | DOI: 10.1007/BF02759700 · Zbl 0127.06704 · doi:10.1007/BF02759700 |
| [8] | DOI: 10.1007/BF01432152 · Zbl 0266.47038 · doi:10.1007/BF01432152 |
| [9] | Jiménez-Sevilla, Studia Math. 127 pp 99– (1998) |
| [10] | DOI: 10.2307/2159836 · Zbl 0803.46024 · doi:10.2307/2159836 |
| [11] | Grothendieck, Canad. J. Math. 5 pp 129– (1953) · Zbl 0050.10902 · doi:10.4153/CJM-1953-017-4 |
| [12] | DOI: 10.1017/S0305004100075435 · Zbl 0774.46019 · doi:10.1017/S0305004100075435 |
| [13] | Diestel, Vector measures (1977) · doi:10.1090/surv/015 |
| [14] | Deville, Smoothness and renormings in Banach spaces (1993) · Zbl 0782.46019 |
| [15] | Choi, J. London Math. Soc. 54 pp 135– (1996) · Zbl 0858.47005 · doi:10.1112/jlms/54.1.135 |
| [16] | Bonsall, Numerical ranges of operators on normed spaces and of elements of normed algebras (1971) · Zbl 0207.44802 · doi:10.1017/CBO9781107359895 |
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