OPERATOR ACCRETIVE KUAT PADA RUANG HILBERT

Razis Aji Saputro, Susilo Hariyanto, YD Sumanto

Abstract


Abstract. Pre-Hilbert space is a vector space equipped with an inner-product. Furthermore, if each Cauchy sequence in a pre-Hilbert space is convergent then it can be said complete and it called as Hilbert space. The accretive operator is a linear operator in a Hilbert space. Accretive operator is occurred if the real part of the corresponding inner product will be equal to zero or positive. Accretive operators are also associated with non-negative self-adjoint operators. Thus, an accretive operator is said to be strict if there is a positive number such that the real part of the inner product will be greater than or equal to that number times to the squared norm value of any vector in the corresponding Hilbert Space. In this paper, we prove that a strict accretive operator is an accretive operator.


Abstrak. Ruang Pre-Hilbert merupakan ruang vektor yang dilengkapi dengan perkalian dalam. Lebih lanjut, apabila setiap barisan Cauchy dalam suatu ruang Pre-Hilbert bersifat konvergen maka ia dapat disebut komplit dan ia disebut ruang Hilbert. Operator accretive merupakan operator linier dalam suatu ruang Hilbert. Operator accretive muncul jika bagian real dari perkalian dalam bernilai nol atau positif. Operator Accretive juga berasosiasi dengan operator non-negative self-adjoint. Kemudian, suatu operator accretive dikatakan kuat jika terdapat bilangan positif sedemikian sehingga bagian real dari perkalian dalam bernilai lebih besar atau sama dengan bilangan tersebut dikalikan nilai norma dikuadratkan dari sebarang vektor dalam ruang Hilbert yang bersangkutan. Dalam artikel ini, dibuktikan bahwa suatu operator accretive kuat juga merupakan operator accretive.


Full Text:

[PDF]

References


MCIntosh, Alan, Functional Calculi. Lashi Bandara, 2010.

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

Kreyszig, Erwin, Introductory Functional Analysis with Application, Wiley Classics Library, 1978.

Berberian, Sterling. K, Introduction to Hilbert Space, New York: Oxford university Press, 1961.




DOI: http://dx.doi.org/10.14710/jfma.v1i1.10

Refbacks

  • There are currently no refbacks.




Copyright (c) 2018 Journal of Fundamental Mathematics and Applications (JFMA)



PUBLISHER:

Department of Mathematics, Faculty of Science and Mathematics, Diponegoro University

Mailing address: Jl. Prof Soedarto, SH, Tembalang, Semarang, Indonesia 50275

Telp./Fax             : +6224 7648 0922

Website              : www.jfma.math.fsm.undip.ac.id

E-mail                : admin.math@live.undip.ac.id

 

INDEXED IN:

Scientific Literature (SCILIT) Google Scholar Garda Rujukan Digital (GARUDA) CROSSREF ROAD ONE SEARCH ID DIMENSIONS