Multiplication operators on the Banach algebra of bounded Φ-variation functions on compact subsets of ℂ

• Autorzy: Bracamonte Mireya , Ereú Jurancy , Marchan Luz

Identyfikatory

DOI

10.1515/dema-2022-0162

• Języki publikacji: EN

Abstrakty

EN

Let AΦ(K) be the Banach algebra of bounded Φ -variation functions defined on a compact set K in the complex plane, h a function defined on K, and Mh a multiplication operator induced by h. In this article, we determine the conditions that h must satisfy for Mh to be an operator that has closed range, finite rank or is compact. We also characterize the conditions that h must satisfy for Mh to be a Fredholm operator.

Słowa kluczowe

EN

Φ-variation; multiplication operators

PL

różnicowanie; operator mnożenia

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2022
• Tom: Vol. 55, nr 1
• Strony: 760--771
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Bracamonte Mireya

• Department of Mathematics, ESPOL Polytechnic University, Escuela Superior Politécnica del Litoral, ESPOL, Facultad de Ciencias Naturales y Matemática, Campus Gustavo Galindo Km. 30.5 Vía Perimetral, P.O. Box 09-01-5863, Guayaquil, Ecuador

autor

Ereú Jurancy

• Department of Mathematics, Universidad Centroccidental Lisandro Alvarado, UCLA, Decanato de Ciencias y Tecnología, Barquisimeto, Venezuela

autor

Marchan Luz

• Department of Mathematics, ESPOL Polytechnic University, Escuela Superior Politécnica del Litoral, ESPOL, Facultad de Ciencias Naturales y Matemática, Campus Gustavo Galindo Km. 30.5 Vía Perimetral, P.O. Box 09-01-5863, Guayaquil, Ecuador

Bibliografia

• [1] M. Bracamonte, J. Ereú, and L. Marchan Luz, The Banach algebra of bounded Φ -variation functions on compact subsets of ℂ, Appl. Math. Inf. Sci. 15 (2021), no. 2, 115–122.
• [2] B. Ashton and I. Doust, Functions of bounded variationon compact subsets of the plane, Studia Math. 169 (2005), 163–188.
• [3] I. Doust and S. Al-shakarchi, Isomorphisms of AC(σ) spaces for countable sets, In: Böttcher, A., Potts, D., Stollmann, P., Wenzel, D. (eds), The Diversity and Beauty of Applied Operator Theory. Operator Theory: Advances and Applications, Birkhäuser, Cham, 268, 2018, 193–206. https://doi.org/10.1007/978-3-319-75996-8_11.
• [4] M. Bracamonte, J. Giménez, and N. Merentes, Vector valued functions of bounded bidimensional Φ-variation, Ann. Funct. Anal. 4, (2013), no. 1, 89–108.
• [5] R. M. Dudley and R. Norvaiša, Concrete Functional Calculus, Springer Monographs in Mathematics, New York, 2011.
• [6] P. Aiena, Semi-Fredholm operators, perturbation theory and localized SVEP, XX Escuela Venezolana de Matemáticas, Mérida - Venezuela, 2007.
• [7] R. Castillo, J. Ramos-Fernández, and H. Vacca-González, Properties of multiplication operators on the space of functions of bounded φ-variation, Open Math. 19 (2021), no. 1, 492–504.
• [8] D. Bugajewski and J. J. Gulgowski, On the characterization of compactness in the space of functions of bounded variation in the sense of Jordan, Math. Anal. Appl. 444 (2016), 230–250.

Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).