Advanced Techniques with Block Matrices of Operators

Preface
Contents
1 Matrices and Hilbert Space Operators
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	1.1 Fundamental Information
	1.2 Some Decompositions of Operators
	1.3 Unitarily Invariant Norms
	1.4 Moore–Penrose Inverse
	1.5 Differences Between Real and Complex Hilbert Spaces
	1.6 Exercises and Problems
2 Block Matrices of Operators
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		2.1 Operator Matrices of Size n times nn timesn
		2.2 Dilation
		2.3 2 times 22times2 Matrices with Entries in a upper C Superscript asteriskC*-Algebra
		2.4 Positivity of 2 times 22times2 Matrices of Operators
		2.5 Diagonal Blocks and Unitary Orbits
		2.6 Inequalities Follow from the Positivity of 2 times 22times2 Block Matrices
		2.7 Inequalities Related to Unitarily Invariant Norms  and Numerical Radius
		2.8 Some Inequalities Involving Eigenvalues and Singular Values
		2.9 Exercises and Problems
3 Operator Monotone Functions and Positive Maps
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	3.1 Operator Monotone and Operator Convex Functions
	3.2 Operator Means
	3.3 Positive and Completely Positive Linear Maps
	3.4 Weakly 22-Positive Maps
	3.5 Positive Linear Maps on Matrix Algebras
	3.6 Exercises and Problems
4 Operator Variance and Covariance
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	4.1 Bounds for the Operator Norm of the Covariance
	4.2 Bounds for Unitarily Invariant Norms of the Covariance
	4.3 Concluding Remarks
	4.4 Exercises and Problems
5 Nonlinear Positive Maps
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	5.1 Lieb Maps and Their Fundamental Properties
	5.2 33-Positivity of Nonlinear Maps
	5.3 Continuity of 33-Positive Maps
	5.4 Exercises and Problems
Bibliography
Index