دانلود کتاب Advanced Techniques with Block Matrices of Operators

فهرست مطالب :

Preface
Contents
1 Matrices and Hilbert Space Operators
[DELETE]
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
[DELETE]
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
[DELETE]
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
[DELETE]
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
[DELETE]
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