Abstract
A general notion of classes of operators between Banach lattices is investigated. It generalizes the definitions and properties of all known special classes of operators (cone absolutely summing, majorizing, p-convex, p-concave and others).
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References
J.A. Abramovič, On the space of operators acting between Banach lattices (Russian), Zap. Naučn. Sem. LOMI 73 (1977), 87–92.
D.I. Cartwright and H.P. Lotz, Some characterizations of AM-and AL-spaces, Math. Z. 142 (1975), 97–103.
J. Chaney, Banach lattices of compact maps, Math. Z. 129 (1972),1–19.
P. Dodds and D.H. Fremlin, Compact operators in Banach lattices, Israel J. Math. 34 (1979), 287–320.
L.P. Janovskij, Summing and order summing operators and characterizations of AL-spaces (Russian), Sibirsk. Mat. Z. 20 (1979), 402–408.
V.L. Levin, Tensor products and functors in categories of Banach spaces generated by KB-lineals (Russian), Trudy Moskov. Mat. Obšč. 20 (1969), 43–81.
J.Lindenstrauss and L.Tzafriri, Classical Banach spaces, II, Function spaces, Berlin-Heidelberg-New York 1979.
B.Maurey, Type et cotype dans les espaces munis de structures locales inconditionelles, Sém. Maurey-Schwartz 1973–74, Exp. 24–25.
P. Mayer-Nieberg, Kegel p-absolutsummierende und p-beschränkende Operatoren, Indag. Math. 40 (1978), 479–490.
N.J.Nielsen, On Banach ideals determined by Banach lattices and their applications, Diss. Math. 109, Warszawa 1973.
P. Ørno, On Banach lattices of operators, Israel J. Math. 19 (1974), 264–265.
A.Pietsch, Operator ideals, Berlin 1978.
N.Popa, Sur les applications du types ⩽p et ⩾p, Preprint Series INCREST 3, Bucuresti 1977.
H.H.Schaefer, Banach lattices and positive operators, Berlin-Heidelberg-New York 1974.
U. Schlotterbeck, Über Klassen majorisierender Operatoren auf Banachverbänden, Revista Acad. Ci. Zaragossa 26 (1971), 585–614.
U.Schlotterbeck, Tensorprodukte von Banachverbänden, Habilitation, Tübingen 1977.
H.-U. Schwarz, Banach lattices of bounded operators,Math. Nachr. 90 (1979), 103–108.
G. Wittstock, Eine Bemerkung über Tensorprodukte von Banachverbänden, Arch. Math. (Basel) 25 (1974),627–634.
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© 1983 Springer-Verlag
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Schwarz, H.U. (1983). Bounded operators in Banach lattices. In: Pietsch, A., Popa, N., Singer, I. (eds) Banach Space Theory and its Applications. Lecture Notes in Mathematics, vol 991. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061574
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DOI: https://doi.org/10.1007/BFb0061574
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