Operator Linear Kontinu Terbatas Pada Ruang Bernorma Cone C0[a; b] KE C[a; b]

Syarifudin, Agus Nur Ahmad (2015) Operator Linear Kontinu Terbatas Pada Ruang Bernorma Cone C0[a; b] KE C[a; b]. Undergraduate thesis, Institut Technology Sepuluh Nopember.

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Abstract

Ruang bernorma cone merupakan perluasan dari ruang bernorma. Perbedaan keduanya terletak pada kodomain fungsi tersebut. Pada fungsi norma, kodomain yang digunakan adalah R tetapi pada fungsi norma cone kodomain yang digunakan adalah sebarang ruang Banach E. Salah satu pembahasan yang menarik untuk dikaji dari ruang bernorma cone adalah operator linear sebab penelitian mengenai operator linear dalam ruang bernorma cone belum banyak dilakukan. Oleh karena itu, dalam tugas akhir ini diselidiki mengenai sifat kekontinuan dan keterbatasan operator linear pada ruang bernorma cone, khususnya operator linear pada ruang bernorma cone C0[a; b] ke C[a; b]. Demikian pula, diperoleh bahwa ruang operator linear terbatas pada ruang bernorma cone C0[a; b] ke C[a; b] merupakan ruang Banach cone. ========================================================================================================= Cone normed space is a generalization of normed space. The di�erence between them is on their codomain's function. On norm function, R is used as its codomain while cone norm function uses any Banach space E. One of the interesting topic of cone normed space is linear operator because of its infrequently in researches. Therefore, in this �nal project we investigated the boundedness and continuity properties of linear operator on cone normed space, especially a linear operator on C0[a; b] cone normed space to C[a; b]. Moreover, we obtained that the bounded linear operators space on C0[a; b] cone normed space to C[a; b] is a Banach cone space.

Item Type: Thesis (Undergraduate)
Additional Information: RSMa 514.325 Sya o
Uncontrolled Keywords: Ruang Banach, Ruang Bernorma, Ruang Bernorma Cone, Operator Linear
Subjects: Q Science > QA Mathematics > QA611.28 Metric spaces
Divisions: Faculty of Mathematics and Science > Mathematics > (S1) Undergraduate Theses
Depositing User: Mr. Tondo Indra Nyata
Date Deposited: 04 Oct 2019 07:34
Last Modified: 04 Oct 2019 07:34
URI: http://repository.its.ac.id/id/eprint/70996

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