QA290 : Projection, Birkho Orthogonality And Angles In Real Normed Linear Spaces
Thesis > Central Library of Shahrood University > Mathematical Sciences > MSc > 2015
Authors:
Hasan Khaje [Author], Mahdi Iranmanesh[Supervisor]
Abstarct: Nowadays, not only concepts orthogonality and angle play very important role at geometric research, but also these concepts are important at analysis research. For this reason, various types of orthogonalities and angles are defined in normed linear spaces. In this thesis, at first we generalized concepts of orthogonality and angle to normed linear spaces and become familar with a variety of orthogonalities and angles. Then we use from this orthogonalities and angles in subjects of charactrizationof inner product spaces and the concept of best approximation. Moreover we try to use Birkhoff orthogonality and concept of best approximation for defintion of oriented angles. At of end we use projections to give a definition of an angle such that this angle have a relation with Birkhoff orthogonality. In the first chapter we introduce theorems and basic concepts. In the second chapter concept of the orthogonality generalized from inner product spaces to normed linear spaces and becom acquainted with some of the orthogonality. Then in this chapter we discuss in deatail about one of the main orthogonality namely Birkhoff orthogonality and finally this chapter we covering to charactrization of inner product spaces with using of orthogonalities specifically Birkhoff orthogonality. In the third chapter we introduce generalized angles in normed linear spaces and become familar with some of the angles including wilson angles and g-angle and then by using these angles we covering charactrization of inner product spaces. In fourth chapter we introduce concepts of othogonality and angle in quasi- inner product spaces and become familar with one of the applications of g-orthogonalities in the best approximation. In the fifth chapter we introduce oriented angles by using of the Birkhoff orthogonality and concept of best approximation. In the sixth chapter in Minkowski plane, we use projections for definition of the q-angle such that this angle have a relation with Birkhoff orthogonality.
Keywords:
#orthogonality #Birkhoff orthogonality #angle #quasi-inner product spaces #best approximation #Minkowski plane #projections Link
Keeping place: Central Library of Shahrood University
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