×

zbMATH — the first resource for mathematics

Isomorphisms and multipliers on second dual algebras of Banach algebras. (English) Zbl 0818.46050
A Banach algebra \(A\) is called weakly completely continuous (w.c.c) if it is a two-sided ideal in \(A''\) the second dual algebra.
The paper begins with some general results concerning multipliers and topological isomorphisms on w.c.c algebras with bounded approximate identities. These results are then applied to the second dual algebra of \(L^ 1(G)\) and various other algebras. The question of the existence of non-zero compact left multipliers on \(L^ 1(G)''\) is studied next. The paper concludes with a list of open problems.

MSC:
46H05 General theory of topological algebras
22D15 Group algebras of locally compact groups
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1112/jlms/s2-37.3.464 · Zbl 0608.43002 · doi:10.1112/jlms/s2-37.3.464
[2] DOI: 10.1112/jlms/s2-41.3.445 · Zbl 0667.43004 · doi:10.1112/jlms/s2-41.3.445
[3] DOI: 10.2307/1998568 · Zbl 0489.43006 · doi:10.2307/1998568
[4] Eymard, Bull. Soc. Math. France 92 pp 181– (1964)
[5] Duncan, Proc. Roy. Soc. Edinburgh Sect. A 84 pp 309– (1979) · Zbl 0427.46028 · doi:10.1017/S0308210500017170
[6] DOI: 10.1007/BF02567327 · Zbl 0211.15502 · doi:10.1007/BF02567327
[7] Bonsall, Complete Normed Algebras (1973) · doi:10.1007/978-3-642-65669-9
[8] DOI: 10.1215/S0012-7094-73-04023-4 · Zbl 0265.46055 · doi:10.1215/S0012-7094-73-04023-4
[9] DOI: 10.1016/0022-1236(81)90062-8 · Zbl 0463.46046 · doi:10.1016/0022-1236(81)90062-8
[10] DOI: 10.2307/2031695 · Zbl 0044.32601 · doi:10.2307/2031695
[11] Akemann, Glasgow Math. J. 21 pp 143– (1980) · Zbl 0462.46040 · doi:10.1017/S0017089500004110
[12] Akemann, Pacific J. Math. 22 pp 1– (1967) · Zbl 0158.14205 · doi:10.2140/pjm.1967.22.1
[13] Watanabe, Sci. Rep. Niigata Univ. Ser. A 2 pp 95– (1974)
[14] DOI: 10.1016/0022-1236(72)90077-8 · Zbl 0242.22010 · doi:10.1016/0022-1236(72)90077-8
[15] DOI: 10.1215/S0012-7094-49-01640-3 · Zbl 0033.18701 · doi:10.1215/S0012-7094-49-01640-3
[16] DOI: 10.1112/jlms/s2-35.1.135 · Zbl 0585.43001 · doi:10.1112/jlms/s2-35.1.135
[17] DOI: 10.1007/BF01169770 · Zbl 0527.46037 · doi:10.1007/BF01169770
[18] DOI: 10.2307/2042364 · Zbl 0415.43003 · doi:10.2307/2042364
[19] Granirer, Ann. Inst. Fourier (Grenoble) 29 pp 37– (1979) · Zbl 0403.46048 · doi:10.5802/aif.765
[20] DOI: 10.2307/2001602 · Zbl 0711.43002 · doi:10.2307/2001602
[21] DOI: 10.1112/blms/20.4.342 · Zbl 0628.43002 · doi:10.1112/blms/20.4.342
[22] DOI: 10.2307/2001412 · Zbl 0682.46037 · doi:10.2307/2001412
[23] DOI: 10.2307/2000861 · Zbl 0634.46041 · doi:10.2307/2000861
[24] Ghahramani, Proc. Edinburgh Math. Soc. 26 pp 343– (1983)
[25] lger, Pacific J. Math. 143 pp 377– (1990) · Zbl 0734.46032 · doi:10.2140/pjm.1990.143.377
[26] DOI: 10.2307/2044211 · Zbl 0489.46040 · doi:10.2307/2044211
[27] Takesaki, Theory of Operator Algebras 1 (1979) · doi:10.1007/978-1-4612-6188-9
[28] DOI: 10.2307/2037854 · Zbl 0258.43010 · doi:10.2307/2037854
[29] Paterson, Amenability (1988) · doi:10.1090/surv/029
[30] DOI: 10.2307/2039232 · Zbl 0284.46041 · doi:10.2307/2039232
[31] DOI: 10.2307/2045771 · Zbl 0595.43003 · doi:10.2307/2045771
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.