Lattice properties of ℒ(E,F)

May, William D.; Chivukula, R. Rao

doi:10.1215/s0012-7094-72-03941-5

Cited by 3 publications

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“…It is shown in particular that if Y is both locally and boundedly order complete, then ^\X, Y) is an /-ideal in L\X, Y). This improves a result of Krengel (see May and Chivukula, 1972).…”

Section: Introductionsupporting

confidence: 82%

“…In particular, if (X, C,||.||) is a normed vector lattice such that the norm ||.|| is additive on C, then the norm-topology coincides with a^X,X'). Therefore the preceding corollary is an improvement of Theorem 1 of May and Chivukula (1972) as well as of Krengel's result (see Peressini, 1967 (IV.3.8), p. 174).…”

Section: Lattice Properties Of Cone-absolutely Summing Mappingsmentioning

confidence: 65%

“…Let r be any ^"-continuous Riesz seminorm on Y. By Lemma 1 of May and Chivukula (1972), there exists a ^"-continuous Riesz seminorm q on Y such that…”

Section: Consequently Se\x Y)<=-l\x Y)mentioning

confidence: 99%

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On majorizing and cone-absolutely summing mappings

Wong

1977

J. Aust. Math. Soc.

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The notions of majorizing mappings and cone-absolutely summing mappings are studied in the locally convex Riesz space setting. It is shown that a locally convex Riesz space Y is an M-space in the sense of Jameson (1970) if and only if, for any locally convex space E, every continuous linear map from E into Y is majorizing. Another purpose of this note is to study the lattice properties of the vector space ℒl(X, Y) of cone-absolutely summing mappings from one locally convex Riesz space into another Y. It is shown that if Y is both locally and boundedly order complete, then ℒl(X, Y) is an l-ideal in Lb(X, Y). This improves a result of Krengel.

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“…It is shown in particular that if Y is both locally and boundedly order complete, then ^\X, Y) is an /-ideal in L\X, Y). This improves a result of Krengel (see May and Chivukula, 1972).…”

Section: Introductionsupporting

confidence: 82%

Section: Lattice Properties Of Cone-absolutely Summing Mappingsmentioning

confidence: 65%