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Introduction to Hilbert Space

Sterling K. Berberian
Publisher: 
American Mathematical Society/Chelsea
Publication Date: 
1961
Number of Pages: 
206
Format: 
Hardcover
Edition: 
2
Price: 
32.00
ISBN: 
0821819127
Category: 
Monograph
BLL Rating: 

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

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Vector Spaces

  • 1. Complex vector spaces
  • 2. First properties of vector spaces
  • 3. Finite sums of vectors
  • 4. Linear combinations of vectors
  • 5. Linear subspaces, linear dependence
  • 6. Linear independence
  • 7. Basis, dimension
  • 8. Coda

Hilbert Spaces

  • 1. Pre-Hilbert spaces
  • 2. First properties of pre-Hilbert spaces
  • 3. The norm of a vector
  • 4. Metric spaces
  • 5. Metric notions in pre-Hilbert space; Hilbert spaces
  • 6. Orthogonal vectors, orthonormal vectors
  • 7. Infinite sums in Hilbert space
  • 8. Total sets, separable Hilbert spaces, orthonormal bases
  • 9. Isomorphic Hilbert spaces; classical Hilbert space

Closed Linear Subspaces

  • 1. Some notations from set theory
  • 2. Annihilators
  • 3. Closed linear subspaces
  • 4. Complete linear subspaces
  • 5. Convex sets, minimizing vector
  • 6. Orthogonal complement
  • 7. Mappings
  • 8. Projection

Continuous Linear Mappings

  • 1. Linear mappings
  • 2. Isomorphic vector spaces
  • 3. The vector space $\scr{L}(\scr{V}, \scr{W})$
  • 4. Composition of mappings
  • 5. The algebra $\scr{L}(\scr{V})$
  • 6. Continuous mappings
  • 7. Normed spaces, Banach spaces, continuous linear mappings
  • 8. The normed space $\scr{L}_c(\scr{E}, \scr{F})$
  • 9. The normed algebra $\scr{L}_c(\scr{E})$, Banach algebras
  • 10. The dual space $\scr{E}^{\prime}$

Continuous Linear Forms in Hilbert Space

  • 1. Riesz-Frechet theorem
  • 2. Completion
  • 3. Bilinear mappings
  • 4. Bounded bilinear mappings
  • 5. Sesquilinear mappings
  • 6. Bounded sesquilinear mappings
  • 7. Bounded sesquilinear forms in Hilbert space
  • 8. Adjoints

Operators in Hilbert Space

  • 1. Manifesto
  • 2. Preliminaries
  • 3. An example
  • 4. Isometric operators
  • 5. Unitary operators
  • 6. Self-adjoint operators
  • 7. Projection operators
  • 8. Normal operators
  • 9. Invariant and reducing subspaces

Proper Values

  • 1. Proper vectors, proper values
  • 2. Proper subspaces
  • 3. Approximate proper values

Completely Continuous Operators

  • 1. Completely continuous operators
  • 2. An example
  • 3. Proper values of CC-operators
  • 4. Spectral theorem for a normal CC-operator
  • Appendix
  • Index

Dummy View - NOT TO BE DELETED