Books > Science & Mathematics > Mathematics > Algebra
|
Buy Now
Lie Algebras of Bounded Operators (Hardcover, 2001 ed.)
Loot Price: R1,700
Discovery Miles 17 000
|
|
Lie Algebras of Bounded Operators (Hardcover, 2001 ed.)
Series: Operator Theory: Advances and Applications, 120
Expected to ship within 10 - 15 working days
|
In several proofs from the theory of finite-dimensional Lie
algebras, an essential contribution comes from the Jordan canonical
structure of linear maps acting on finite-dimensional vector
spaces. On the other hand, there exist classical results concerning
Lie algebras which advise us to use infinite-dimensional vector
spaces as well. For example, the classical Lie Theorem asserts that
all finite-dimensional irreducible representations of solvable Lie
algebras are one-dimensional. Hence, from this point of view, the
solvable Lie algebras cannot be distinguished from one another,
that is, they cannot be classified. Even this example alone urges
the infinite-dimensional vector spaces to appear on the stage. But
the structure of linear maps on such a space is too little
understood; for these linear maps one cannot speak about something
like the Jordan canonical structure of matrices. Fortunately there
exists a large class of linear maps on vector spaces of arbi trary
dimension, having some common features with the matrices. We mean
the bounded linear operators on a complex Banach space. Certain
types of bounded operators (such as the Dunford spectral, Foia
decomposable, scalar generalized or Colojoara spectral generalized
operators) actually even enjoy a kind of Jordan decomposition
theorem. One of the aims of the present book is to expound the most
important results obtained until now by using bounded operators in
the study of Lie algebras."
General
Is the information for this product incomplete, wrong or inappropriate?
Let us know about it.
Does this product have an incorrect or missing image?
Send us a new image.
Is this product missing categories?
Add more categories.
Review This Product
No reviews yet - be the first to create one!
|
|
Email address subscribed successfully.
A activation email has been sent to you.
Please click the link in that email to activate your subscription.