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.
Reihe
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Illustrationen
Maße
Höhe: 235 mm
Breite: 155 mm
ISBN-13
978-81-85931-89-0 (9788185931890)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
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.
