Notes on functional analysis
著者
書誌事項
Notes on functional analysis
（Texts and readings in mathematics, 50）
Hindustan Book Agency, c2009
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
These notes are a record of a one semester course on Functional Analysis given by the author to second year Master of Statistics students at the Indian Statistical Institute, New Delhi. Students taking this course have a strong background in real analysis, linear algebra, measure theory and probability, and the course proceeds rapidly from the definition of a normed linear space to the spectral theorem for bounded selfadjoint operators in a Hilbert space. The book is organised as twenty six lectures, each corresponding to a ninety minute class session. This may be helpful to teachers planning a course on this topic. Well prepared students can read it on their own.
目次
- Lecture 1: Banach Spaces.
- Lecture 2: Dimensionality.
- Lecture 3: New Banach Spaces from Old.
- Lecture 4: The Hahn-Banach Theorem.
- Lecture 5: The Uniform Boundedness Principle.
- Lecture 6: The Open Mapping Theorem.
- Lecture 7: Dual Spaces.
- Lecture 8: Some Applications.
- Lecture 9: The Weak Topology.
- Lecture 10: The Second Dual and the Weak* Topology.
- Lecture 11: Hilbert Spaces.
- Lecture 12: Orthonormal Bases.
- Lecture 13: Linear Operators.
- Lecture 14: Adjoint Operators.
- Lecture 15: Some Special Operators in Hilbert Space.
- Lecture 16: The Resolvent and The Spectrum.
- Lecture 17: Subdivision of the Spectrum.
- Lecture 18: Spectra of Normal Operators.
- Lecture 19: Square Roots and the Polar Decomposition.
- Lecture 20: Compact Operators.
- Lecture 21: The Spectrum of a Compact Operator.
- Lecture 22: Compact Operators and Invariant Subspaces.
- Lecture 23: Trace Ideals.
- Lecture 24: The Spectral Theorem - I.
- Lecture 25: The Spectral Theorem - II.
- Lecture 26: The Spectral Theorem - III.
- Index.
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