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## Studia Mathematica

2013 | 218 | 1 | 55-88
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### New examples of K-monotone weighted Banach couples

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Some new examples of K-monotone couples of the type (X,X(w)), where X is a symmetric space on [0,1] and w is a weight on [0,1], are presented. Based on the property of w-decomposability of a symmetric space we show that, if a weight w changes sufficiently fast, all symmetric spaces X with non-trivial Boyd indices such that the Banach couple (X,X(w)) is K-monotone belong to the class of ultrasymmetric Orlicz spaces. If, in addition, the fundamental function of X is $t^{1/p}$ for some p ∈ [1,∞], then $X = L_{p}$. At the same time a Banach couple (X,X(w)) may be K-monotone for some non-trivial w in the case when X is not ultrasymmetric. In each of the cases where X is a Lorentz, Marcinkiewicz or Orlicz space, we find conditions which guarantee that (X,X(w)) is K-monotone.
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Tom
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55-88
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2013
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autor
• Department of Mathematics and Mechanics, Samara State University, Acad. Pavlova 1, 443011 Samara, Russia
autor
• Department of Engineering Sciences and Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden
• Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G2G1, Canada
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