M. S. Moslehian is a professor of Mathematics at Ferdowsi University of Mashhad, a member of the Academy of Sciences of Iran, a TWAS fellow, and the president of the Iran. Math. Soc. His research focuses on functional analysis, operator theory, and matrix analysis. He has served as a senior associate at ICTP (Italy) and as a visiting professor at various universities in England, Sweden, and Japan. He is also the editor-in-chief of the journals "Banach J. Math. Anal.", "Ann. Funct. Anal.", and "Adv. Oper. Theory" published by Birkhäuser/Springer.Hiroyuki Osaka is a professor in the Department of Mathematical Sciences at Ritsumeikan University, Japan. His research concerns operator algebras, operator theory, and quantum information theory. He was a postdoctoral researcher at Fields Institute (Canada), an assistant research professor at Copenhagen University (Denmark), an associate professor at Ryukyu University (Japan), and a visiting professor at several universities in the USA, India, and Poland. He is an editor of "Adv. Oper. Theory" published by Birkhäuser/Springer and "Sci. Math. Jpn." published by Inst. Soc. Math. Sci.

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• Preface.- 1 Matrices and Hilbert Space Operators.- 2 Block Matrices of Operators.- 3 Operator Monotone Functions and Positive Maps.- 4 Operator Variance and Covariance.- 5 Nonlinear Positive Maps.- Bibliography.

M. S. Moslehian is a professor of Mathematics at Ferdowsi University of Mashhad, a member of the Academy of Sciences of Iran, a TWAS fellow, and the president of the Iran. Math. Soc. His research focuses on functional analysis, operator theory, and matrix analysis. He has served as a senior associate at ICTP (Italy) and as a visiting professor at various universities in England, Sweden, and Japan. He is also the editor-in-chief of the journals "Banach J. Math. Anal.", "Ann. Funct. Anal.", and "Adv. Oper. Theory" published by Birkhäuser/Springer.Hiroyuki Osaka is a professor in the Department of Mathematical Sciences at Ritsumeikan University, Japan. His research concerns operator algebras, operator theory, and quantum information theory. He was a postdoctoral researcher at Fields Institute (Canada), an assistant research professor at Copenhagen University (Denmark), an associate professor at Ryukyu University (Japan), and a visiting professor at several universities in the USA, India, and Poland. He is an editor of "Adv. Oper. Theory" published by Birkhäuser/Springer and "Sci. Math. Jpn." published by Inst. Soc. Math. Sci.

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• Preface.- 1 Matrices and Hilbert Space Operators.- 2 Block Matrices of Operators.- 3 Operator Monotone Functions and Positive Maps.- 4 Operator Variance and Covariance.- 5 Nonlinear Positive Maps.- Bibliography.