Author | Farenick, Douglas R. author |
---|---|
Title | Algebras of Linear Transformations [electronic resource] / by Douglas R. Farenick |
Imprint | New York, NY : Springer New York, 2001 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-0097-7 |
Descript | XIV, 240 p. online resource |
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