Measure of weak noncompactness and real interpolation of operators

By A. Kryczka, S. Prus, Mariusz Szczepanik. Bulletin of the Australian Mathematical Society, 2000

51 citations recorded by the source corpus.

A new measure of weak noncompactness is introduced. A logarithmic convexity-type result on the behaviour of this measure applied to bounded linear operators under real interpolation is proved. In particular, it gives a new proof of the theorem showing that if at least one of the operators T: Ai → Bi, i = 0, 1 is weakly compact, then so is T : Aθ,p → Bθ,p for all 0 < θ < 1 and 1 < P < ∞.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b22cb34ff381778c98d120b3afa84a3926093326

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In Applied Mathematics

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In Mathematical Physics

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Citations in the corpus

• Measures of weak noncompactness in Banach spaces (2009, background): “Measures of noncompactness or weak noncompactness have been successfully applied in operator theory, differential equations and integral equations, see for instance [1, 3, 4, 9, 14, 15] and [16].”