Joint similarity problems and the generation of operator algebras with bounded length Academic Article

abstract

• There is a pair of commuting operators (T1, T2) on Hilbert space such that each T1 and T2 is similar to a contraction but the pair (T1, T2) is not similar to a pair of contractions. There is a pair of commuting unitarizable representations (1, 2) on the free group with N 2 generators such that (1, 2) is not similar to a pair of unitary representations. In connection with these examples, we introduce and study a notion of "length" for a C *-algebra (or an operator algebra) generated by two subalgebras, which is analogous to the minimum length of a word in the generators of a group.

authors

• Pisier, Gilles

published proceedings

• INTEGRAL EQUATIONS AND OPERATOR THEORY

author list (cited authors)

• Pisier, G.

citation count

• 14

complete list of authors

• Pisier, G

publication date

• September 1998

publisher

• Springer Nature  Publisher

published in

• Integral Equations and Operator Theory  Journal

keywords

• 49 Mathematical Sciences
• 4902 Mathematical Physics
• 4904 Pure Mathematics

Digital Object Identifier (DOI)

• 10.1007/BF01195125

start page

• 353

end page

• 370

volume

• 31

issue

• 3

URL

• http://dx.doi.org/10.1007/bf01195125