×

zbMATH — the first resource for mathematics

\(L\)-weakly and \(M\)-weakly compact operators. (English) Zbl 1028.47028
From the introduction: Because of the difficulties of studying weakly compact operators in a general Banach lattice setting, a number of related notions have been studied in the literature. Two of these are the dual notions of \(L\)-weak compactness and \(M\)-weak compactness. In this paper, we investigate some properties of these classes of operators.

MSC:
47B60 Linear operators on ordered spaces
46B42 Banach lattices
47B07 Linear operators defined by compactness properties
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Aliprantis, C.D.; Burkinshaw, O., Factoring compact and weakly compact operators through reflexive Banach lattices, Trans. amer. math. soc., 283, 369-381, (1984) · Zbl 0521.47017
[2] Aliprantis, C.D.; Burkinshaw, O., Positive operators, (1985), Academic Press New York and London · Zbl 0567.47037
[3] Abramovich, Y.A.; Wickstead, A.W., A compact regular operator without modulus, (), 721-726 · Zbl 0781.47036
[4] Abramovich, Y.A.; Wickstead, A.W., Solutions of several problems in the theory of compact positive operators, (), 3021-3026 · Zbl 0860.47023
[5] Abramovich, Y.A.; Wickstead, A.W., When each continuous operator is regular, Indag math., 8, 281-294, (1997) · Zbl 0908.47031
[6] Cartwright, D.I.; Lotz, H.P., Some characterizations of AM- and A1-spaces, Math. Z., 142, 97-103, (1975) · Zbl 0285.46009
[7] Chen, Z.L.; Wickstead, A.W., Relative weak compactness of solid hulls in Banach lattices, Indag. math., 9, 187-196, (1998) · Zbl 0922.46017
[8] Chen, Z.L. and A.W. Wickstead — Vector lattices of weakly compact operators between Banach lattices. Trans. Amer. Math. Soc. (To appear).
[9] Dodds, P.G.; Fremlin, D.H., Compact operators in Banach lattices, Israel J. maths., 34, 287-320, (1979) · Zbl 0438.47042
[10] Krengel, U., Remark on the modulus of compact operators, Bull. amer. math. soc., 72, 132-133, (1966) · Zbl 0135.36302
[11] Meyer-Nieberg, P., Banach lattices, (1991), Springer Verlag Berlin, Heidelberg, New York · Zbl 0743.46015
[12] Niculescu, C.P., Weak compactness in Banach lattices, J. oper. theory, 6, 217-231, (1981) · Zbl 0498.46017
[13] Popa, I., Espaces de Banach réticulés ayant la propriété de Schur, C.R. acad. sci. Paris, 285, 629-631, (1977) · Zbl 0372.46009
[14] Räbiger, F., Dunford-Pettis operators on certain classes of Banach lattices, Semesterbericht funktional analysis, tubingen, 15, 197-204, (1988-1989)
[15] Wnuk, W., Some characterisations of Banach lattices with the Schur property, Revista mat., 2, 217-224, (1989) · Zbl 0717.46018
[16] Wnuk, W., Banach spaces with properties of the Schur type — a survey, (), 1-25 · Zbl 0812.46010
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.