Journal of Fundamental Mathematics and Applications (JFMA)
Vol 1, No 2 (2018): Journal of Fundamental Mathematics and Applications

OPERATOR PADA RUANG FUNGSI TERINTEGRAL DUNFORD

Solikhin, Solikhin (Unknown)
Sumanto, YD (Unknown)
Hariyanto, Susilo (Unknown)
Aziz, Abdul (Unknown)



Article Info

Publish Date
29 Nov 2018

Abstract

Artikel ini membahas tentang integral Dunford dan operator pada ruang fungsi terintegral Dunford. Diperoleh hasil bahwa ruang fungsi yang terintegral Dunford merupakan ruang linear. Untuk setiap fungsi   yang terintegral Dunford pada $[a,b]$, maka operator $T$  dengan formula $T\left( {{x}^{*}} \right)={{x}^{*}}\left( f \right)$ merupakan operator linear terbatas dan operator kompak lemah. Sedangkan operator adjoint , dengan rumus ${{T}^{*}}\left( g \right)\left( {{x}^{*}} \right)=\int\limits_{a}^{b}{g{{x}^{*}}\left( f \right)}$ juga merupakan operator linear terbatas dan kompak lemah. Operator  kompak lemah jika dan hanya jika operator adjoint ${{T}^{*}}$ kompak lemah. Lebih lanjut $\left\| {{T}^{*}} \right\|=\left\| T \right\|$.

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Journal Info

Abbrev

jfma

Publisher

Subject

Control & Systems Engineering Decision Sciences, Operations Research & Management Mathematics

Description

Journal of Fundamental Mathematics and Applications (JFMA), formerly known as Jurnal Matematika dan Komputer, is an indonesian journal published by Department of Mathematics, Diponegoro University, Semarang, Indonesia. In every year, JFMA has been published regularly in 2 scheduled times (on June ...