ISOMETRIC AND ISOMETRIC- m OPERATORS

Gunawan Gunawan(1*),

(1) Pendidikan Matematika, FKIP, Universitas Muhammadiyah Purwokerto
(*) Corresponding Author


Abstract


This paper presents the definition, samples, and natures of isometric and isometric- m algebra operator for some  in  Hilbert space. In additions, the relationship of both operators will also be examined. To investigate natures of isometric and isometric- m operators, adjoint operators concepts and natures are required. Adjoint operator concept underlies isometric operator’s natures. Later, according to the concept, isometrc operator is expanded into isometric- m operators for some in Hilbert space. The result unveils algebra natures of isometric and isometric- m operators consisting of composition operators natures and multiplication with scalar. Furthermore, if T operators is isometric then T operators isometric- m for some .


Keywords


Adjoint Operators; Isometric Operators; Isometric- m Operators

References


Akhiezer, N.I. and Glazman, M. 2013. Theory of Linear Operators in Hilbert Spaces. New York: Dover Publication, Inc.

Berberian, S.K.1961. Introduction to Hilbert Spaces. New York: Oxford University Press.

Kreyszig, E.1978. Introductory Functional Analysis with Applications. New York: John Wiley and Sons.

Saddi, Adel and Ould Ahmed Mahmoud Sid Ahmed . 2010. m- Partial Isometries On Hilbert Spaces. Internat J. Functional Analysis, Operator Theory,and Applications . Volume 2, No 1, Pages 67-83, 7 September. Dapat diakses di http://pphmj.com/journals/ijaota.htm.




DOI: http://dx.doi.org/10.24127/ajpm.v6i3.1081

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