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"Salah satu bahan yang dibahas di ruang vektor adalah keortogonalan antara dua vektor. Konsep keortogonalan umumnya dikenal di ruang hasil kali dalam. Di ruang ber-norm terdapat konsep keortogonalan Pythagoras, sama kaki (Isosceles), dan Birkhoff James. Kemudian, Gahler memperkenalkan ruang ber-norm-2 dan ruang hasil kali dalam-2. Di tesis ini, dibahas konsep keortogonalan Pythagoras, sama kaki, dan Birkhoff James di ruang ber-norm-2 dan konsep keortogonalan-G di ruang hasil kali dalam-2. Kemudian, dibahas hubungan keekuivalenan antara konsep keortogonalan Pythagoras, sama kaki, dan Birkhoff James di ruang ber-norm-2. ......Orthogonality is one of the main topic in a vector space. Orthogonality of 2 vectors is generally known in inner product space. In normed space, there are Pythagorean, isosceles, and Birkhoff James orthogonality. Later, Gahler introduced a 2-normed space and a 2-inner product space. In this thesis, we discuss about Pythagorean, isosceles, and Birkhoff James orthogonality in a 2-normed space and G-orthogonality in a 2-inner product space. Then, we discuss the equivalency relations between Pythagorean, isosceles and Birkhoff James orthogonality in 2-normed space."

"Teori spektral adalah salah satu cabang utama dari analisis fungsional. Dalam teori spektral, dipelajari mengenai operator-operator inversi dari operator linear. Yang diperhatikan adalah sifat-sifat umumnya dan hubungan dengan operator linear aslinya. Dalam teori spektral, dikenal dua himpunan yang saling bebas yaitu spektrum dan himpunan resolvent. Operator linear yang diperhatikan pada skripsi ini adalah operator linear terbatas dan operator linear self adjoint terbatas yang telah dikenal di analisis fungsional. Sifat spektrum dan himpunan resolvent dari kedua operator linear tersebut menjadi hal utama yang dikaji di skripsi ini. ......Spectral theory is one of the main branches of functional analysis. Spectral theory is study about the inverse operators of linear operator. It is concerned with their general properties and their relations to the original linear operator. In spectral theory, there are two adjoint sets called spectrum and resolvent set. There are two linear operators in this undergraduate thesis, they are bounded linear operator and bounded self adjoint linear operator from functional analysis. Spectrum and resolvent set properties of those linear operators is the main part of this undergraduate thesis."