On \(A\)-orthogonally diagonalizable operators on semi-inner product spaces
Authors
R. Respitawulan
- Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi, Bandung, Indonesia.
F. Yuliawan
- Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi, Bandung, Indonesia.
H. Garminia
- Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi, Bandung, Indonesia.
P. Astuti
- Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi, Bandung, Indonesia.
Abstract
In finite dimensional inner product (IP) spaces, any self-adjoint operator is normal and any normal operator is orthogonally diagonalizable. However, in semi-inner product (SIP) spaces, there exists an \(A\)-self-adjoint operator which is not \(A\)-normal. Therefore, it is interesting to study conditions for an \(A\)-self-adjoint operator on an SIP space to be \(A\)-orthogonally diagonalizable. An SIP is a mapping induced by a positive semi-definite operator on an IP space. In this paper, we study necessary, sufficient, and necessary and sufficient conditions for an \(A\)-self-adjoint operator to be \(A\)-orthogonally diagonalizable.
Share and Cite
ISRP Style
R. Respitawulan, F. Yuliawan, H. Garminia, P. Astuti, On \(A\)-orthogonally diagonalizable operators on semi-inner product spaces, Journal of Mathematics and Computer Science, 36 (2025), no. 3, 290--298
AMA Style
Respitawulan R. , Yuliawan F., Garminia H., Astuti P., On \(A\)-orthogonally diagonalizable operators on semi-inner product spaces. J Math Comput SCI-JM. (2025); 36(3):290--298
Chicago/Turabian Style
Respitawulan, R. , Yuliawan, F., Garminia, H., Astuti, P.. "On \(A\)-orthogonally diagonalizable operators on semi-inner product spaces." Journal of Mathematics and Computer Science, 36, no. 3 (2025): 290--298
Keywords
- Semi-inner product spaces
- spectral decomposition
- \(A\)-self-adjoint operators
MSC
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