منابع مشابه
Topological aspects of dynamics of pairs, tuples and sets
Topological theory of dynamical systems concentrates on study of qualitative aspects of dynamics of continuous transformations by various topological tools (many of them are borrowed from other fields such as algebra or measure theory). The aim of this chapter is to present, by no means complete, an exposition on local aspects of dynamics of pairs, or more generally tuples and sets. It is motiv...
متن کاملUnitary N-dilations for Tuples of Commuting Matrices
We show that whenever a contractive k-tuple T on a finite dimensional space H has a unitary dilation, then for any fixed degree N there is a unitary k-tuple U on a finite dimensional space so that q(T ) = PHq(U)|H for all polynomials q of degree at most N .
متن کاملLengths of quasi-commutative pairs of matrices
In this paper we discuss some partial solutions of the length conjecture which describes the length of a generating system for matrix algebras. We consider mainly the algebras generated by two matrices which are quasi-commuting. It is shown that in this case the length function is linearly bounded. We also analyze which particular natural numbers can be realized as the lengths of certain specia...
متن کاملPairs of Matrices with Property L(0
1. It was proved by Frobenius [l] that any function f(A, B) of two commutative «X« square matrices A, B has as characteristic roots the numbers /(X¿, Hi) where X¿ are the characteristic roots of A and pi the characteristic roots of B, both taken in a special ordering independent of the function /. However, commutativity of A and B is known not to be a necessary condition [2]. Matrices which hav...
متن کاملOn Pairs of Commuting Nilpotent Matrices
Let B be a nilpotent matrix and suppose that its Jordan canonical form is determined by a partition λ. Then it is known that its nilpotent commutator NB is an irreducible variety and that there is a unique partition μ such that the intersection of the orbit of nilpotent matrices corresponding to μ with NB is dense in NB. We prove that map D given by D(λ) = μ is an idempotent map. This answers a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1972
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1972.40.639