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HILBERT SPACESInner Product Spaces and Hilbert SpacesJordan-Neuman TheoremOrthogonal Decomposition of Hilbert SpaceGram-Schmidt Orthonormal Procedure and its ApplicationsFUNDAMENTAL PROPERTIES OF BOUNDED LINEAR OPERATIONSBounded Linear Operations on Hilbert SpacePartial Isometry Operator and Polar Decomposition of an OperatorPolar Decomposition of an Operator and its ApplicationsSpectrum of an OperatorNumerical Range of an OperatorRelations Among Several Classes of Non-normal OperatorsCharacterizations of Convexoid Operators and Related ExamplesFURTHER DEVELOPMENT OF BOUNDED LINEAR OPERATORSYoung Inequality and Holder-McCarthy InequalityLowner-Heinz Inequality and Furuta InequalityChaotic Order and the Relative Operator EntropyAluthge Transformation on P-Hyponormal Operators and Log-Hyponormal OperatorsA Subclass of Paranormal Operators Including Loh-Hyponormal Operators and Several Related ClassesOperator Inequalities Associated With Kantorovich Inequality and Holder-McCarthy InequalitySome Properties on Partial Isometry, Quasinormality and ParanormalityWeighted Mixed Schwarz Inequality and Generalized Schwarz InequalitySelberg InequalityAn Extension of Heinz-Kato InequalityNorm Inequalities Equivalent to Lower-Heinz InequalityNorm Inequalities Equivalent to Heinz InequalityBibliographyIndex