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Functional Analysis: Entering Hilbert Space

Af: Vagn Lundsgaard Hansen Engelsk Hardback

Functional Analysis: Entering Hilbert Space

Af: Vagn Lundsgaard Hansen Engelsk Hardback
Tjek vores konkurrenters priser

 

Reviews of the First Edition:

“This is a well-written student-friendly basic introduction to functional analysis and Hilbert space …”

MAA Online Book Review

 

“The highlight of the book is the spectral theorem for selfadjoint linear compact operators, presented with full proof. The book ends with a set of well chosen exercises completing the main text.”

Zentralblatt MATH

 

This book presents basic elements of the theory of Hilbert spaces and operators on Hilbert spaces, culminating in a proof of the spectral theorem for compact, self-adjoint operators on separable Hilbert spaces. It exhibits a construction of the space of pth power Lebesgue integrable functions by a completion procedure with respect to a suitable norm in a space of continuous functions, including proofs of the basic inequalities of Hölder and Minkowski. The Lp-spaces thereby emerges in direct analogy with a construction of the real numbers from the rational numbers. This allows grasping the main ideas more rapidly. Other important Banach spaces arising from function spaces and sequence spaces are also treated.

In this second edition, I have expanded the material on normed vector spaces and their operators presented in Chapter 1 to include proofs of the Open Mapping Theorem, the Closed Graph Theorem and the Hahn–Banach Theorem.

The material on operators between normed vector spaces is further expanded in a new Chapter 6, which presents the basic elements of the theory of Fredholm operators on general Banach spaces, not only on Hilbert spaces. This requires that we develop the theory of dual operators between Banach spaces to replace the use of adjoint operators between Hilbert spaces.

With the addition of the new material on normed vector spaces and their operators, the book can serve as a general introduction to functional analysis viewed as a theory of infinite dimensional linear spaces and linear operators acting on them.

Tjek vores konkurrenters priser
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Tjek vores konkurrenters priser

 

Reviews of the First Edition:

“This is a well-written student-friendly basic introduction to functional analysis and Hilbert space …”

MAA Online Book Review

 

“The highlight of the book is the spectral theorem for selfadjoint linear compact operators, presented with full proof. The book ends with a set of well chosen exercises completing the main text.”

Zentralblatt MATH

 

This book presents basic elements of the theory of Hilbert spaces and operators on Hilbert spaces, culminating in a proof of the spectral theorem for compact, self-adjoint operators on separable Hilbert spaces. It exhibits a construction of the space of pth power Lebesgue integrable functions by a completion procedure with respect to a suitable norm in a space of continuous functions, including proofs of the basic inequalities of Hölder and Minkowski. The Lp-spaces thereby emerges in direct analogy with a construction of the real numbers from the rational numbers. This allows grasping the main ideas more rapidly. Other important Banach spaces arising from function spaces and sequence spaces are also treated.

In this second edition, I have expanded the material on normed vector spaces and their operators presented in Chapter 1 to include proofs of the Open Mapping Theorem, the Closed Graph Theorem and the Hahn–Banach Theorem.

The material on operators between normed vector spaces is further expanded in a new Chapter 6, which presents the basic elements of the theory of Fredholm operators on general Banach spaces, not only on Hilbert spaces. This requires that we develop the theory of dual operators between Banach spaces to replace the use of adjoint operators between Hilbert spaces.

With the addition of the new material on normed vector spaces and their operators, the book can serve as a general introduction to functional analysis viewed as a theory of infinite dimensional linear spaces and linear operators acting on them.

Produktdetaljer
Sprog: Engelsk
Sider: 192
ISBN-13: 9789814733922
Indbinding: Hardback
Udgave:
ISBN-10: 981473392X
Udg. Dato: 28 jan 2016
Længde: 0mm
Bredde: 0mm
Højde: 0mm
Forlag: World Scientific Publishing Co Pte Ltd
Oplagsdato: 28 jan 2016
Forfatter(e): Vagn Lundsgaard Hansen
Forfatter(e) Vagn Lundsgaard Hansen


Kategori Funktionsanalyse og transformation


ISBN-13 9789814733922


Sprog Engelsk


Indbinding Hardback


Sider 192


Udgave


Længde 0mm


Bredde 0mm


Højde 0mm


Udg. Dato 28 jan 2016


Oplagsdato 28 jan 2016


Forlag World Scientific Publishing Co Pte Ltd

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