Porosity and products of Orlicz spaces

Akbarbaglu, Ibrahim; Maghsoudi, S.

doi:10.1007/s11117-012-0218-0

Cited by 4 publications

(1 citation statement)

References 9 publications

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“…Remark 18.40. In the papers [25], [41], [6] some extensions of presented results are obtained -instead of L p spaces there are considered Orlicz spaces and Lorentz spaces. Also, multiplication of n functions is considered, for any fixed n ∈ N (instead of just two).…”

Section: The Next Results Shows What Happens Ifmentioning

confidence: 98%

Bilinear mappings – selected properties and problems

Balcerzak¹,

Strobin²,

Wachowicz³

2013

Traditional and Present-Day Topics in Real Analysis. Dedicated to Professor Jan Stanisław Lipiński

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This work is a survey of results and problems connected with selected properties of bilinear mappings between function spaces. Section 1 is devoted to the lack of the counterpart of the Banach openness principle for bilinear surjections between Banach spaces. Some counterexamples and positive results are discussed. Then we deal with variants of openness for multiplication in spaces C(K), for a compact K, and in other Banach algebras and function spaces. In Section 2, several phenomena of dichotomies for operators of multiplication and convolution in spaces of integrable or continuous functions are presented. Some natural properties of these operators hold either always or the sets of objects having the given property are small. The smallness is described by meagerness and porosity. Let us introduce some basic notation. The ball with center x and radius r in a given metric space X is denoted by B X (x, r) (if X is fixed, index X will be omitted). The interior of a set A ⊂ X will be written as int(A).

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Section: The Next Results Shows What Happens Ifmentioning

confidence: 98%