- Tytuł:
- On a theorem of Gelfand and its local generalizations
- Autorzy:
- Drissi, Driss
- Powiązania:
- https://bibliotekanauki.pl/articles/1220142.pdf
- Data publikacji:
- 1997
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
locally power-bounded operator
local spectrum
local spectral radius - Opis:
- In 1941, I. Gelfand proved that if a is a doubly power-bounded element of a Banach algebra A such that Sp(a) = {1}, then a = 1. In [4], this result has been extended locally to a larger class of operators. In this note, we first give some quantitative local extensions of Gelfand-Hille's results. Secondly, using the Bernstein inequality for multivariable functions, we give short and elementary proofs of two extensions of Gelfand's theorem for m commuting bounded operators, $T_1,..., T_m$, on a Banach space X.
- Źródło:
-
Studia Mathematica; 1997, 123, 2; 185-194
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł