HUDU

Algebras of Linear Transformations


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gebunden
Lieferbar innerhalb von 2-3 Tagen
Oktober 2000

Beschreibung

Beschreibung

This book studies algebras and linear transformations acting on finite -dimensional vector spaces over arbitrary fields. It is written for students who have prior knowledge of algebra and linear algebra. The goal is to present a balance of theory and example in order for students to gain a firm understanding of the basic theory of finite- dimensional algebras and to provide a foundation for subsequent advanced study in a number of areas of mathematics. As such, the level of exposition is suitable for senior undergraduate students.

Inhaltsverzeichnis

1. Linear Algebra.
- 1.1 Vector Spaces and Duality.
- 1.2 Direct Sums and Quotients.
- 1.3 Inner-Product Spaces.
- 1.4 The Spectral Theorem.
- 1.5 Fields and Field Extensions.
- 1.6 Existence of Bases for Infinite-Dimensional Spaces.
- 1.7 Notes.
- 1.8 Exercises.
- 2. Algebras.
- 2.1 Algebrai c Structures.
- 2.2 Algebras with a Prescribed Basis.
- 2.3 Algebras of Linear Transformations.
- 2.4 Inversion and Spectra.
- 2.5 Division Algebras and Other Simple Algebras.
- 2.6 Notes.
- 2.7 Exercises.
- 3. Invariant Subspaces.
- 3.1 The Invariant-Subspace Lattice.
- 3.2 Idempotents and Projections.
- 3.3 Existence of Invariant Subspaces.
- 3.4 Representations and Left Ideals.
- 3.5 Functional Calculus and Polar Decomposition.
- 3.6 Notes.
- 3.7 Exercises.
- 4. Semisimple Algebras.
- 4.1 Nilpotent Algebras and the Nil Radical.
- 4.2 Structure of Semisimple Algebras.
- 4.3 Structure of Simple Algebras.
- 4.4 Isomorphism Classes of Semisimple Algebras.
- 4.5 Notes.
- 4.6 Exercises.
- 5. Operator Algebras.
- 5.1 Von Neumann Algebras.
- 5.2 Real and Complex Involutive Algebras.
- 5.3 Representation of Operator Algebras.
- 5.4 Wedderburn Theorems for Operator Algebras.
- 5.5 C*-Algebras.
- 5.5 Notes.
- 5.7 Exercises.
- 6. Tensor Products.
- 6.1 Free Vector Spaces.
- 6.2 Tensor Products of Vector Spaces.
- 6.3 Tensor Products of Algebras.
- 6.4 Tensor Products of Operator Algebras.
- 6.5 Notes.
- 6.6 Exercises.- References.

Innenansichten

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EAN: 9780387950624
ISBN: 0387950621
Untertitel: 2001. Auflage. Book. Sprache: Englisch.
Verlag: Springer
Erscheinungsdatum: Oktober 2000
Seitenanzahl: 260 Seiten
Format: gebunden
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