Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2020, Cilt: 69 Sayı: 2, 1146 - 1160, 31.12.2020
https://doi.org/10.31801/cfsuasmas.752148

Öz

Kaynakça

  • Alaminos, J., Brešar, M., Extremera, J., Villena, A. R., Maps preserving zero products, Studia Math., 193 (2) (2009), 131-159.
  • Alaminos, J., Brešar, M., Spenko, S., Villena A. R., Orthogonally additive polynomials and orthosymmetric maps in Banach algebras with properties A and B, Proceedings of the Edinburgh Mathematical Society, 59 (3) (2016), 559-568.
  • Alaminos, J., Extremera, J., Godoy, M. L. C., Villena, A. R., Orthogonally additive polynomials on convolution algebras associated with a compact group, J Math Anal Appl., 472 (1) (2019),285-302.
  • Ben Amor, F., On orthosymmetric bilinear maps, Positivity, 14 (2010), 123-134.
  • Benyamini, Y., Lassalle, S., Llavona, J. G., Homogeneous orthogonally additive polynomials on Banach lattices, Bull Lond Math Soc., 383 (2006), 459-469.
  • Boulabiar, K., Buskes, G., Vector lattice powers: f-algebras and functional calculus, Comm Algebra., 344 (2006), 1435-1442.
  • Bu, Q., Buskes, G., Kusraev, A. G., Bilinear Maps on Products of Vector Lattices: A Survey, In: Boulabiar K., Buskes G., Triki A. (eds) Positivity. Trends in Mathematics, (2007), 97--126.
  • Defant, A., Floret, K., Tensor norms and operator ideals, North-Holland Math. Stud. Vol. 176, North-Holland, Amsterdam, Elsevier, 1993.
  • Diestel, J., Jarchow H., Tonge, A., Absolutely Summing Operators, Vol. 43. Cambridge University Press, 1995.
  • Dineen, S., Complex Analysis on Infinite Dimensional Spaces, Springer-Verlag, London, 1999.
  • Erdoğan, E., Calabuig, J. M., Sánchez Pérez, E. A., Convolution-continuous bilinear operators acting in Hilbert spaces of integrable functions, Ann. Funct. Anal., 9 (2) (2018), 166-179.
  • Erdoğan, E.(2020): Factorization of multilinear operators defined on products of function spaces, Linear and Multilinear Algebra, https://dx.doi.org/10.1080/03081087.2020.1715334
  • Erdoğan, E., Gök, Ö., Convolution Factorability of Bilinear Maps and Integral Representations, Indag. Math., 29 (5) (2018), 1334-1349.
  • Erdoğan, E., Sánchez Pérez, E. A., Gök, Ö., Product factorability of integral bilinear operators on Banach function spaces, Positivity, 23 (3) (2019), 671-696.
  • Ibort, A., Linares, P., Llavona, J.G., A representation theorem for orthogonally additive polynomials on Riesz spaces, Rev Mat Complut., 251 (2012), 21-30.
  • Sundaresan, K., Geometry of spaces of polynomials on Banach lattices in: Applied Geometry and Discrete Mathematics, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., Amer. Math. Soc., Providence RI, vol 4 (1991), pp 571-586.

Product factorable multilinear operators defined on sequence spaces

Yıl 2020, Cilt: 69 Sayı: 2, 1146 - 1160, 31.12.2020
https://doi.org/10.31801/cfsuasmas.752148

Öz

We prove a factorization theorem for multilinear operators acting in topological products of spaces of (scalar) p-summable sequences through a product. It is shown that this class of multilinear operators called product factorable maps coincides with the well-known class of the zero product preserving operators. Due to the factorization, we obtain compactness and summability properties by using classical functional analysis tools. Besides, we give some isomorphisms between spaces of linear and multilinear operators, and representations of some classes of multilinear maps as n-homogeneous orthogonally additive polynomials.

Kaynakça

  • Alaminos, J., Brešar, M., Extremera, J., Villena, A. R., Maps preserving zero products, Studia Math., 193 (2) (2009), 131-159.
  • Alaminos, J., Brešar, M., Spenko, S., Villena A. R., Orthogonally additive polynomials and orthosymmetric maps in Banach algebras with properties A and B, Proceedings of the Edinburgh Mathematical Society, 59 (3) (2016), 559-568.
  • Alaminos, J., Extremera, J., Godoy, M. L. C., Villena, A. R., Orthogonally additive polynomials on convolution algebras associated with a compact group, J Math Anal Appl., 472 (1) (2019),285-302.
  • Ben Amor, F., On orthosymmetric bilinear maps, Positivity, 14 (2010), 123-134.
  • Benyamini, Y., Lassalle, S., Llavona, J. G., Homogeneous orthogonally additive polynomials on Banach lattices, Bull Lond Math Soc., 383 (2006), 459-469.
  • Boulabiar, K., Buskes, G., Vector lattice powers: f-algebras and functional calculus, Comm Algebra., 344 (2006), 1435-1442.
  • Bu, Q., Buskes, G., Kusraev, A. G., Bilinear Maps on Products of Vector Lattices: A Survey, In: Boulabiar K., Buskes G., Triki A. (eds) Positivity. Trends in Mathematics, (2007), 97--126.
  • Defant, A., Floret, K., Tensor norms and operator ideals, North-Holland Math. Stud. Vol. 176, North-Holland, Amsterdam, Elsevier, 1993.
  • Diestel, J., Jarchow H., Tonge, A., Absolutely Summing Operators, Vol. 43. Cambridge University Press, 1995.
  • Dineen, S., Complex Analysis on Infinite Dimensional Spaces, Springer-Verlag, London, 1999.
  • Erdoğan, E., Calabuig, J. M., Sánchez Pérez, E. A., Convolution-continuous bilinear operators acting in Hilbert spaces of integrable functions, Ann. Funct. Anal., 9 (2) (2018), 166-179.
  • Erdoğan, E.(2020): Factorization of multilinear operators defined on products of function spaces, Linear and Multilinear Algebra, https://dx.doi.org/10.1080/03081087.2020.1715334
  • Erdoğan, E., Gök, Ö., Convolution Factorability of Bilinear Maps and Integral Representations, Indag. Math., 29 (5) (2018), 1334-1349.
  • Erdoğan, E., Sánchez Pérez, E. A., Gök, Ö., Product factorability of integral bilinear operators on Banach function spaces, Positivity, 23 (3) (2019), 671-696.
  • Ibort, A., Linares, P., Llavona, J.G., A representation theorem for orthogonally additive polynomials on Riesz spaces, Rev Mat Complut., 251 (2012), 21-30.
  • Sundaresan, K., Geometry of spaces of polynomials on Banach lattices in: Applied Geometry and Discrete Mathematics, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., Amer. Math. Soc., Providence RI, vol 4 (1991), pp 571-586.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Ezgi Erdoğan 0000-0002-0641-1930

Yayımlanma Tarihi 31 Aralık 2020
Gönderilme Tarihi 13 Haziran 2020
Kabul Tarihi 6 Temmuz 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 69 Sayı: 2

Kaynak Göster

APA Erdoğan, E. (2020). Product factorable multilinear operators defined on sequence spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(2), 1146-1160. https://doi.org/10.31801/cfsuasmas.752148
AMA Erdoğan E. Product factorable multilinear operators defined on sequence spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Aralık 2020;69(2):1146-1160. doi:10.31801/cfsuasmas.752148
Chicago Erdoğan, Ezgi. “Product Factorable Multilinear Operators Defined on Sequence Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, sy. 2 (Aralık 2020): 1146-60. https://doi.org/10.31801/cfsuasmas.752148.
EndNote Erdoğan E (01 Aralık 2020) Product factorable multilinear operators defined on sequence spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 2 1146–1160.
IEEE E. Erdoğan, “Product factorable multilinear operators defined on sequence spaces”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 69, sy. 2, ss. 1146–1160, 2020, doi: 10.31801/cfsuasmas.752148.
ISNAD Erdoğan, Ezgi. “Product Factorable Multilinear Operators Defined on Sequence Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/2 (Aralık 2020), 1146-1160. https://doi.org/10.31801/cfsuasmas.752148.
JAMA Erdoğan E. Product factorable multilinear operators defined on sequence spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:1146–1160.
MLA Erdoğan, Ezgi. “Product Factorable Multilinear Operators Defined on Sequence Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 69, sy. 2, 2020, ss. 1146-60, doi:10.31801/cfsuasmas.752148.
Vancouver Erdoğan E. Product factorable multilinear operators defined on sequence spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(2):1146-60.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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