Notes on functional analysis [electronic resource] / Rajiendra Bhatia.

Call Number	510
Author	Bhatia, Rajiendra.
Title	Notes on functional analysis Rajiendra Bhatia.
Edition	1st ed.
Publication	[S.l.] : Hindustan Book Agency, 2009.
Physical Description	254 p.
Series	Texts and Readings in Mathematics ; 50
Contents	Notes on functional analysis -- Preface -- A Word About Notation -- Contents -- 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 -- Texts and Readings in Mathematics.
Summary	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.
Subject	FUNCTIONAL ANALYSIS MATHEMATICS
Multimedia	https://portal.igpublish.com/iglibrary/search/HBAB0000026.html

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$a 254 p.

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$a Includes bibliographical references and index.

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$a Notes on functional analysis -- Preface -- A Word About Notation -- Contents -- 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 -- Texts and Readings in Mathematics.

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$a 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.

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$a FUNCTIONAL ANALYSIS

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$a MATHEMATICS

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$a Texts and Readings in Mathematics ; $v 50

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Summary	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.
Contents	Notes on functional analysis -- Preface -- A Word About Notation -- Contents -- 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 -- Texts and Readings in Mathematics.
Subject	FUNCTIONAL ANALYSIS MATHEMATICS
Multimedia	https://portal.igpublish.com/iglibrary/search/HBAB0000026.html