LEFT INVERTIBLE SEMIGRUP PADA RUANG HILBERT

Ezhari Asfa’ani, Lilis Harianti Hasibuan, Miftahul Jannah, Darvi Mailisa Putri

Abstract


Analisis Fungsional merupakan salah satu cabang dari ilmu Matematika yang membahas tentang ruang vektor serta pemetaan di antara ruang - ruang tersebut. Pada artikel ini membahas tentang semigrup pada ruang Hilbert yang dapat dibalik dan mempunyai balikan. Untuk Semigrup yang sangat kontinu pada Ruang Hilbert, disini disajikan bukti singkat dari fakta-fakta bahwa inverse kiri dari semigrup yang dapat dibalik dan dapat dipilih menjadi semigrup juga. Lebih jauh pada tulisan ini akan ditunjukkan pula bahwa semigrup ini tidak perlu unik.

Abstract

Functional Analysis is one branch of Mathematics that deals with vector spaces and mapping between these spaces This article to discuss about semigroups on Hilbert Space. For strongly continous semigroups on Hilbert space, we present a short proof of the fact that the left inverse of a left invertible semigroup can be chosen to be a semigroups as well. Furthermore, we show that this semigroups need not to be unique.Keywords: three-five word(s) or phrase(s), that it’s  representative for the article.

Keywords


semigrup, ruang Hilbert, invers kiri

Full Text:

PDF


DOI: https://doi.org/10.15548/map.v2i1.1640
Abstract views : 193 times
PDF : 67 times

References


R.F. Curtain., H.J. Zwart. 1995. An Introduction to Infinite-Dimensional Linear System Theory, Springer-Verlag. New York.

B.H. Haak, E.M.Ouhabaz, Exact Observability, square function, 2012, J.Func Anal, 262(6), 8(2), pp.2903-2927

M. Haase, 2004. Decomposition theorem for generator of strongly continuos groups on Hilbert spaces, J.Operator Theory, 52(1),pp 21-37

J.C. Louis, D.Wexler.1983. On Exact Controllability In Hilbert Spaces. Jurnal of Differential Equation. 49,pp 258-269.

G.Q.Xu, C. Liu, Y.F. Shang.2000. Characteristic of Left invertible semigroups and admissibility of observasion operation, System and Control Letters, 58(8),pp. 561-566.

. G.Q. Xu, Y.F.Shang, Characteristic of left invertible semigroups and admissibility of abservation operators,System and Contol Letters, 58(8),pp. 561-566,2009

Darmawijaya, Soeparna. 2007. Pengantar Analisis Abstrak. UGM, Yogyakarta.

F. Kappel, W. Schappacher: Strongly continuous semigroups–an introduction, preprint. 5.


Refbacks

  • There are currently no refbacks.


Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

 

Lisensi Creative Commonsis licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.