Ortogonalitas di Ruang Bernorm
DOI:
https://doi.org/10.24256/jpmipa.v1i1.51Keywords:
Ortogonalitas, Ruang bernormAbstract
Ortogonalitas merupakan salah satu konsep yang penting di ruang hasil kali dalam. Sementara itu, ortogonalitas di ruang bernorm belum dikenal secara umum. Akan tetapi, ada beberapa tipe ortogonalitas di ruang bernorm yang telah dikembangkan, yaitu ortogonalitas-BJ, -I, dan –P. Demikian halnya di ruang bernorm-2 terdapat konsep ortogonalitas-D. Pada makalah ini, dipaparkan secara singkat sifat-sifat dasar dari keempat ortogonalitas tersebut yang meliputi sifat nondegenerasi, simetri, homogen, aditif kanan, resolvabilitas, dan kontinuitas. Keekivalenan antara keempat ortogonalitas ini dengan ortogonalitas biasa di ruang hasil kali dalam juga dipaparkan dalam akhir makalah ini.References
Gunawan, H., Mashadi, Gemawati, S., Nursupiamin, Sihwaningrum, I., 2006, Orthogonality in 2-Normed Spaces Revisited, Univ. Beograd. Publ. Electrotehn. Fak. Ser. Mat. 17, 76-83.
Khan, A., Siddiqui, A., 1982, B-orthogonality in 2-Normed Spaces, Bull. Cal. Math. Soc. 74, 216-222.
Nursupiamin, 2003, Ortogonalitas-BJ, -I, -P, dan –D di Ruang Bernorm (Tesis), Institut Teknologi Bandung.
Partington, J.R., 1986, Orthogonality in Normed Spaces, Bull. Austral. Math. Soc. 33, 449-455.
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