Some remarks on the interpolation spaces A θ , A θ

Mohammad Daher

Commentationes Mathematicae Universitatis Carolinae (2016)

  • Volume: 57, Issue: 3, page 301-315
  • ISSN: 0010-2628

Abstract

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Let ( A 0 , A 1 ) be a regular interpolation couple. Under several different assumptions on a fixed A β , we show that A θ = A θ for every θ ∈ ( 0 , 1 ) . We also deal with assumptions on A ¯ β , the closure of A β in the dual of ( A 0 * , A 1 * ) β .

How to cite

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Daher, Mohammad. "Some remarks on the interpolation spaces $A^\theta , A_\theta $." Commentationes Mathematicae Universitatis Carolinae 57.3 (2016): 301-315. <http://eudml.org/doc/286825>.

@article{Daher2016,
abstract = {Let $(A_0, A_1)$ be a regular interpolation couple. Under several different assumptions on a fixed $A^\{\beta \}$, we show that $A^\{\theta \} = A_\{\theta \}$ for every $\theta \in (0, 1)$. We also deal with assumptions on $\overline\{A\}^\{\beta \}$, the closure of $A^\{\beta \}$ in the dual of $(A_0^*, A_1^*)_\beta $.},
author = {Daher, Mohammad},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {interpolation},
language = {eng},
number = {3},
pages = {301-315},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Some remarks on the interpolation spaces $A^\theta , A_\theta $},
url = {http://eudml.org/doc/286825},
volume = {57},
year = {2016},
}

TY - JOUR
AU - Daher, Mohammad
TI - Some remarks on the interpolation spaces $A^\theta , A_\theta $
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2016
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 57
IS - 3
SP - 301
EP - 315
AB - Let $(A_0, A_1)$ be a regular interpolation couple. Under several different assumptions on a fixed $A^{\beta }$, we show that $A^{\theta } = A_{\theta }$ for every $\theta \in (0, 1)$. We also deal with assumptions on $\overline{A}^{\beta }$, the closure of $A^{\beta }$ in the dual of $(A_0^*, A_1^*)_\beta $.
LA - eng
KW - interpolation
UR - http://eudml.org/doc/286825
ER -

References

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  2. Bergh J., Lofström J., Interpolation Spaces. An Introduction, Springer, Berlin-Heidelberg-New York, 1976. Zbl0344.46071MR0482275
  3. Bergh J., 10.1512/iumj.1979.28.28054, Indiana Univ. Math. J. 28 (1979), 775–777. Zbl0394.41004MR0542336DOI10.1512/iumj.1979.28.28054
  4. Daher M., Une remarque sur l’espace A θ , C.R.Acad. Sci. Paris Ser. I Math. 322 (1996), no. 7, 641–644. MR1386467
  5. Daher M., 10.4064/cm123-2-3, Colloq. Math. 123 (2011), no. 2, 197–204. MR2811171DOI10.4064/cm123-2-3
  6. Daher M., Une remarque sur les espaces d'interpolation faiblement localement uniformément convexes, arXiv:1206.4848. 
  7. Diestel J., Uhl J.J., Vector Measures, Mathematical Surveys, 15, American Mathematical Society, Providence, Rhode Island, 1977. Zbl0521.46035MR0453964
  8. Edgar G.A., 10.1512/iumj.1977.26.26053, Indiana Univ. Math. J. 26 (1977), no. 4, 663–677. Zbl0418.46034MR0487448DOI10.1512/iumj.1977.26.26053
  9. Fabian M., Habala P., Hajek P., Montesinos V., Zizler V., Banach Space Theory, CMS Books in Mathematics, Springer, New York, 2011. Zbl1321.00042MR2766381
  10. Rosenthal H.P., 10.2307/2373824, Amer. J. Math. 99 (1977), no. 2, 362–378. MR0438113DOI10.2307/2373824

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