Author	Halmos, P. R. author
Title	A Hilbert Space Problem Book [electronic resource] / by P. R. Halmos
Imprint	New York, NY : Springer US, 1974
Connect to	http://dx.doi.org/10.1007/978-1-4615-9976-0
Descript	online resource

From the Preface: "This book was written for the active reader. The first part consists of problems, frequently preceded by definitions and motivation, and sometimes followed by corollaries and historical remarks... The second part, a very short one, consists of hints... The third part, the longest, consists of solutions: proofs, answers, or contructions, depending on the nature of the problem.... This is not an introduction to Hilbert space theory. Some knowledge of that subject is a prerequisite: at the very least, a study of the elements of Hilbert space theory should proceed concurrently with the reading of this book."

Problem -- 1. Vectors and Spaces -- 2. Weak Topology -- 3. Analytic Functions -- 4. Infinite Matrices -- 5. Boundedness and Invertibility -- 6. Multiplication Operators -- 7. Operator Matrices -- 8. Properties of Spectra -- 9. Examples of Spectra -- 10. Spectral Radius -- 11. Norm Topology -- 12. Strong and Weak Topologies -- 13. Partial Isometries -- 14. Unilateral Shift -- 15. Compact Operators -- 16. Subnormal Operators -- 17. Numerical Range -- 18. Unitary Dilations -- 19. Commutators of Operators -- 20. Toeplitz Operators -- Hint -- 1. Vectors and Spaces -- 2. Weak Topology -- 3. Analytic Functions -- 4. Infinite Matrices -- 5. Boundedness and Invertibility -- 6. Multiplication Operators -- 7. Operator Matrices -- 8. Properties of Spectra -- 9. Examples of Spectra -- 10. Spectral Radius -- 11. Norm Topology -- 12. Strong and Weak Topologies -- 13. Partial Isometries -- 14. Unilateral Shift -- 15. Compact Operators -- 16. Subnormal Operators -- 17. Numerical Range -- 18. Unitary Dilations -- 19. Commutators of Operators -- 20. Toeplitz Operators -- Solution -- 1. Vectors and Spaces -- 2. Weak Topology -- 3. Analytic Functions -- 4. Infinite Matrices -- 5. Boundedness and Invertibility -- 6. Multiplication Operators -- 7. Operator Matrices -- 8. Properties of Spectra -- 9. Examples of Spectra -- 10. Spectral Radius -- 11. Norm Topology -- 12. Strong and Weak Topologies -- 13. Partial Isometries -- 14. Unilateral Shift -- 15. Compact Operators -- 16. Subnormal Operators -- 17. Numerical Range -- 18. Unitary Dilations -- 19. Commutators of Operators -- 20. Toeplitz Operators -- References