Measure of weak noncompactness under complex interpolation

Andrzej Kryczka; Stanisław Prus

Studia Mathematica (2001)

  • Volume: 147, Issue: 1, page 89-102
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Andrzej Kryczka, and Stanisław Prus. "Measure of weak noncompactness under complex interpolation." Studia Mathematica 147.1 (2001): 89-102. <http://eudml.org/doc/284727>.

@article{AndrzejKryczka2001,
abstract = {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.},
author = {Andrzej Kryczka, Stanisław Prus},
journal = {Studia Mathematica},
keywords = {logarithmic convexity; complex interpolation; linear operator; measure of a weak noncompactness; Calderón’s complex interpolation},
language = {eng},
number = {1},
pages = {89-102},
title = {Measure of weak noncompactness under complex interpolation},
url = {http://eudml.org/doc/284727},
volume = {147},
year = {2001},
}

TY - JOUR
AU - Andrzej Kryczka
AU - Stanisław Prus
TI - Measure of weak noncompactness under complex interpolation
JO - Studia Mathematica
PY - 2001
VL - 147
IS - 1
SP - 89
EP - 102
AB - 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.
LA - eng
KW - logarithmic convexity; complex interpolation; linear operator; measure of a weak noncompactness; Calderón’s complex interpolation
UR - http://eudml.org/doc/284727
ER -

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