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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2020 / Volume: 49 Issue: 6

Embedding the weighted space $Hv_0(G, E)$ of holomorphic functions into the sequence space $c_0(E)$

El Mustapha El Abbassi(Mohammed V University of Rabat)0000-0002-1865-6118
Lahbib Oubbı(Mohammed V University of Rabat)0000-0003-2119-9293
Sayfa
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Yayın Tarihi
2020-12-08
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

We then deduce the non 1-Hyers-Rassias stability of the isometry functional equation in the framework of Banach spaces.

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Amaç & Hipotez:We embed almost isometrically the generalized weighted space $Hv_0(G, E)$ of holomorphic functions on an open subset $G$ of $\mathbb{C}^N$ with values in a Banach space $E$, into $c_0(E)$, the space of all null sequences in $E$, where $v$ is an operator-valued continuous function on $G$ vanishing nowhere.
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Temel Bulgular & Veri:This extends and generalizes some known results in the literature.
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Sonuç & Katkı:We then deduce the non 1-Hyers-Rassias stability of the isometry functional equation in the framework of Banach spaces.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Weighted spaces of holomorphic functions · Vector-valued holomorphic function · Operator-valued weights

Abstract

We embed almost isometrically the generalized weighted space $Hv_0(G, E)$ of holomorphic functions on an open subset $G$ of $\mathbb{C}^N$ with values in a Banach space $E$, into $c_0(E)$, the space of all null sequences in $E$, where $v$ is an operator-valued continuous function on $G$ vanishing nowhere. This extends and generalizes some known results in the literature. We then deduce the non 1-Hyers-Rassias stability of the isometry functional equation in the framework of Banach spaces.

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Bu Makaleye Atıf Yap

Abbassi, E. M. E., Oubbı, L. (2020). Embedding the weighted space $Hv_0(G, E)$ of holomorphic functions into the sequence space $c_0(E)$. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 6. https://doi.org/10.15672/hujms.621628

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Kaynakça (14)

  1. J. Bonet and J.A. Conejero, The sets of monomorphisms and of almost open operators between locally convex spaces, Proc. Amer. Math. Soc. 129, 3683–3690, 2001.
  2. J. Bonet and E. Wolf, A note on weighted Banach spaces of holomorphic functions, Arch. Math. (Basel) 81, 650–654, 2003.
  3. C. Boyd and P. Rueda, The v-boundary of weighted spaces of holomorphic functions, Ann. Acad. Sci. Fenn. Math. 30, 337–352, 2005.
  4. Z. Gajda, On stability of additive mappings, Int. J. Math. Math. Sci. 14, 431–434, 1991.
  5. H.A. Gindler and A.E. Taylor, The minimum modulus of a linear operator and its use in spectral theory, Studia Math. 22, 15–41, 1962.
  6. L. Hörmander, An Introduction to Complex Analysis in Several Variables, North- Holland Mathematical Library 7, North-Holland, 1990.
  7. M. Klilou and L. Oubbi, Multiplication operators on generalized weighted spaces of continuous functions, Mediterr. J. Math. 13, 3265–3280, 2016.
  8. M. Klilou and L. Oubbi, Weighted composition operators on Nachbin spaces with operator-valued weights, Commun. Korean Math. Soc. 33, 1125–1140, 2018
  9. W. Lusky, On the structure of $H_{v_0}(D)$ and $h_{v_0}(D)$, Math. Nachr. 159, 279–289, 1992.
  10. W. Lusky, On weighted spaces of harmonic and holomorphic functions, J. London Math. Soc. 51, 309–320, 1995.
  11. W. Lusky, On the isomorphism classes of weighted spaces of harmonic and holomorphic functions, Studia Math. 175, 19–45, 2006.
  12. V. Müller, Spectral theory of linear operators and spectral systems in Banach algebras, in: Operator Theory: Advances and Applications, second ed. 139, Birkhäuser Verlag, Basel, 2007.
  13. W. Rudin, Function Theory in the Unit Ball of $\mathbb{C}^n$, Classics in Mathematics, Springer Berlin, 1980.
  14. C. Shekhar and B.S. Komal, Multiplication operators on weighted spaces of continuous functions with operator-valued weights, Int. J. Contemp. Math. Sci. 7 (38), 1889–1894, 2012.