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.
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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 > 44201-(S1) Undergraduate Thesis |
| 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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