Measure of weak noncompactness under complex interpolation

• Autorzy: Andrzej Kryczka , Stanisław Prus
• Języki publikacji: EN

Abstrakty

EN

Logarithmic convexity of a measure of weak noncompactness for bounded linear operators under Calderón's complex interpolation is proved. This is a quantitative version for weakly noncompact operators of the following: if T: A₀ → B₀ or T: A₁ → B₁ is weakly compact, then so is $T:A_{[θ]} → B_{[θ]}$ for all 0 < θ < 1, where $A_{[θ]}$ and $B_{[θ]}$ are interpolation spaces with respect to the pairs (A₀,A₁) and (B₀,B₁). Some formulae for this measure and relations to other quantities measuring weak noncompactness are established.

Kategorie tematyczne

• 46B70: Interpolation between normed linear spaces
• 46M35: Abstract interpolation of topological vector spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2001
• Tom: 147
• Numer: 1
• Strony: 89-102

Daty

wydano

2001

Twórcy

autor

Andrzej Kryczka

• Institute of Mathematics, Maria Curie-Skłodowska University, 20-031 Lublin, Poland

autor

Stanisław Prus

• Institute of Mathematics, Maria Curie-Skłodowska University, 20-031 Lublin, Poland

Identyfikatory

DOI

10.4064/sm147-1-7