Operator Adjoint pada Ruang Fungsi Terintegral Dunford
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Published
Feb 28, 2020
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Abstract
Artikel ini mengkaji integral Dunford fungsi bernilai Banach . Jika fungsi merupakan fungsi terukur lemah sedemikian sehingga fungsi terintegral Lebesgue, maka fungsi tersebut dikatakan terintegral Dunford. Nilai integral Dunford atas sebarang himpunan terukur adalah . Diperlihatkan bahwa koleksi semua fungsi terintegral Dunford, merupakan ruang linear. Jika untuk setiap didefinisikan operator oleh , untuk setiap , maka merupakan operator Adjoint dari operator . Ditunjukan bahwa operator Adjoint merupakan operator linear dan terbatas. Selanjutnya dikaji beberapa sifat yang lain dari operator Adjointnya.
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Solikhin, S., Hariyanto, S., Sumanto, Y., & Aziz, A. (2020). Operator Adjoint pada Ruang Fungsi Terintegral Dunford. PRISMA, Prosiding Seminar Nasional Matematika, 3, 34-40. Retrieved from https://journal.unnes.ac.id/sju/prisma/article/view/37545
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References
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Solikhin, dkk. (2018). Operator pada Ruang Fungsi Terintegral Dunford. Journal of Fundamental Mathematics and Application (JFMA), 2(1), 110-121.
Cao, S. C., (1992). The Henstock Integral for Banach-valued Functions. Southeast Asian Bull. Math, 16(1), 35-40.
Cao, S. C., (1993). On The Henstock-Bochner Integral. Southeast Asian Bull. Math. Special Issue, p. 1-3.
Darmawijaya, S. (2007). Pengantar Analisis Abstrak. Jurusan Matematika Fakultas MIPA Universitas Gadjah Mada, Yogyakarta.
Gordon, R.A. (1994). The Integral of lebesgue, Denjoy, Perron, and Henstock. Mathematical Society, USA.
Guoju, Ye., & Tianqing, An. (2001). On Henstock-Dunford and Henstock-Pettis Integrals. IJMMS, 25(7), 467-478.
Guoju, Ye. (2007). On Henstock–Kurzweil and McShane integrals of Banach space-valued functions. J. Math. Anal. Appl. 330 (-) 753–765.
Kreyszig, E. (1989). Introductory Funtional Analysis with Applications. John Willey & Sons, USA.
Lee, P. Y. (1989). Lanzhou Lectures on Henstock Integration. World Scientific, Singapore.
Park, at al. (2006). The Henstock-Pettis integral of Banach Space-valued functions. Journal of the Chungcheong mathematical society, 19(3), 231-236.
Saifullah. (2003). Integral Henstock-Dunford pada Ruang Euclide Rn. Tesis, Universitas Gadjah Mada, Yogyakarta.
Schwabik, S., & Guoju, Ye. (2005). Topics in Banach Space Integration. World Scientific, Singapore.
Solikhin, dkk. (2018). Operator pada Ruang Fungsi Terintegral Dunford. Journal of Fundamental Mathematics and Application (JFMA), 2(1), 110-121.