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On inclusion relations between Lorentz sequence spaces and inequalities of Lewis type. (English) Zbl 0594.46006

Summary: The Lorentz sequence spaces \(\ell_{p,q}\) and the relations \(\ell_{p,q}\subset \ell_{p_ 1,q}\) if \(1\leq p<p_ 1\leq \infty\) and \(\ell_{p,q}\subset \ell_{p,q_ 1}\) if \(1\leq p\leq \infty\), \(1\leq q\leq q_ 1<\infty\) are well known. In this paper a generalization of these spaces is considered using the symmetric norming functions of R. Schatten and some inclusion relations are presented. In the second part of the paper these inclusion relations are utilised to establish inequalities of Lewis type for some operator ideals generated by an additive s-function (s-number).

MSC:

46A45 Sequence spaces (including Köthe sequence spaces)
46B25 Classical Banach spaces in the general theory
47L10 Algebras of operators on Banach spaces and other topological linear spaces
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