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Some characterizations of AM- and AL-spaces. (English) Zbl 0285.46009


MSC:

46A40 Ordered topological linear spaces, vector lattices
47B60 Linear operators on ordered spaces
47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
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References:

[1] Bennett, G.: Some ideals of operators on Hilbert space, Preprint · Zbl 0338.47013
[2] Bose, R.C., Chowla, S.: Theorems in the additive theory of numbers, Commentarii math. Helvet.37, 141-147 (1962/63) · Zbl 0109.03301 · doi:10.1007/BF02566968
[3] Kantorovitch, L.V.: Sur la théorie générale des opérations dans les espaces semiordonnés, C.r. Acad. Sci., URSS (N. S.)1, 283-286 (1936)
[4] Krengel, U.: Über den Absolutbetrag stetiger linearer Operatoren und seine Anwendung auf ergodische Zerlegungen, Math. Scandinav.13, 151-187 (1963) · Zbl 0201.16702
[5] Kwapie?, S., Pelczy?ski, A.: The main triangle projection in matrix spaces and its applications, Studia math.34, 43-68 (1970)
[6] Lotz, H.P.: AL-spaces, AM-spaces and Grothendieck’s Fundamental Theorem, Preprint
[7] Pietsch, A.: Nukleare lokalkonvexe Räume, Berlin: Akademie-Verlag 1965 · Zbl 0152.32302
[8] Schaefer, H.H.: Normed tensor products of Banach lattices, Israel J. Math.13, 400-415 (1972) · Zbl 0252.46095 · doi:10.1007/BF02762813
[9] Schaefer, H.H.: Topological Vector Spaces. Berlin-Heidelberg-New York: Springer 1971 · Zbl 0212.14001
[10] Schlotterbeck, U.: Über Klassen majorisierbarer Operatoren in Banachverbänden, Revista Acad. Ci. exact. fis.-quim. natur. Zaragoza, II. Ser.26, 585-614 (1971) · Zbl 0294.47020
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