- Tytuł:
- On operator bands
- Autorzy:
-
Drnovšek, Roman
Livshits, Leo
MacDonald, Gordon W.
Mathes, Ben
Radjavi, Heydar
Šemrl, Peter - Powiązania:
- https://bibliotekanauki.pl/articles/1206129.pdf
- Data publikacji:
- 2000
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
invariant subspaces
idempotents
operator semigroups - Opis:
- A multiplicative semigroup of idempotent operators is called an operator band. We prove that for each K>1 there exists an irreducible operator band on the Hilbert space $l^2$ which is norm-bounded by K. This implies that there exists an irreducible operator band on a Banach space such that each member has operator norm equal to 1. Given a positive integer r, we introduce a notion of weak r-transitivity of a set of bounded operators on a Banach space. We construct an operator band on $l^2$ that is weakly r-transitive and is not weakly (r+1)-transitive. We also study operator bands S satisfying a polynomial identity p(A, B) = 0 for all non-zero A,B ∈ S, where p is a given polynomial in two non-commuting variables. It turns out that the polynomial $p(A, B) = (A B - B A)^2$ has a special role in these considerations.
- Źródło:
-
Studia Mathematica; 2000, 139, 1; 91-100
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł